All Implemented Interfaces:

JxnCloneableAlgebra
```
public class JxnComplexAlgebra
extends Object
implements JxnCloneableAlgebra
```
Implementation of a complex algebra. Stores real and imaginary part with double precision. Supports mixed operations with double, JxnRealArrayAlgebra and JxnComplexArrayAlgebra.

Call one of the plot methods to visualize complex values as phasors (arrows) in a PlotFrame.

Field Summary

Fields
Modifier and Type	Field	Description
`protected static int`	`defaultNDec`	Default nDec for `toString()`.
`protected static double`	`equalityTolerance`	Tolerance for `equals` method.
`double`	`im`	Imaginary part.
`protected static JxnComplexAlgebra`	`J`	`j`.
`protected static JxnComplexAlgebra`	`JJJ`	`-j`.
`protected static JxnComplexAlgebra`	`ONE`	`1 + j 0`.
`double`	`re`	Real part.

Constructor Summary

Constructors
Constructor	Description
`JxnComplexAlgebra()`	Creates `j`.
`JxnComplexAlgebra(double re)`	Creates `re + j 0`.
`JxnComplexAlgebra(double re, double im)`	Creates `re + j im`.
`JxnComplexAlgebra(double r, double phi, boolean deg)`	Creates complex from magnitude `r` and phase angle `phi`.
`JxnComplexAlgebra(JxnComplexAlgebra z)`	Creates a copy of `z`.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method	Description
`static double`	`abs(JxnComplexAlgebra z)`	Returns the absolute value (magnitude) of `z`.
`static JxnComplexAlgebra`	`acos(JxnComplexAlgebra z)`	Return the inverse cosine of `z`.
`static JxnComplexAlgebra`	`acosh(JxnComplexAlgebra z)`	Return the inverse hyperbolic cosine of `z`.
`JxnComplexAlgebra`	`add(double d)`	Adds `d` to this.
`JxnComplexAlgebra`	`add(JxnComplexAlgebra z)`	Adds `z` to this.
`JxnComplexArrayAlgebra`	`add(JxnComplexArrayAlgebra ca)`	Returns `ca` added to this.
`JxnComplexArrayAlgebra`	`add(JxnRealArrayAlgebra ra)`	Returns `ra` added to this.
`static KmgComplexAngle`	`angle(JxnComplexAlgebra center, double radius, double startAngle, double tipAngle, String label, Color color)`	See `angle`.
`static KmgComplexAngle`	`angle(JxnComplexAlgebra center, double radius, double startAngle, double tipAngle, String label, Color color, boolean d90)`	See `angle`.
`static KmgComplexAngle`	`angle(JxnComplexAlgebra phiStart, JxnComplexAlgebra phiTip, double radFak, String label, Color color)`	See `angle`.
`static KmgComplexAngle`	`angle(JxnComplexAlgebra phiStart, JxnComplexAlgebra phiTip, double radFak, String label, Color color, boolean d90)`	See `angle`.
`static KmgComplexAngle`	`angle(JxnComplexAlgebra center, JxnComplexAlgebra phiStart, JxnComplexAlgebra phiTip, double radFak, String label, Color color)`	Returns an angle (arc with arrow tip).
`static KmgComplexAngle`	`angle(JxnComplexAlgebra center, JxnComplexAlgebra phiStart, JxnComplexAlgebra phiTip, double radFak, String label, Color color, boolean d90)`	See `angle`.
`static double`	`arg(JxnComplexAlgebra z)`	Returns the argument (phase angle) of `z` (duplicates `phi(z)`).
`static double`	`argD(JxnComplexAlgebra z)`	Returns the argument (phase angle) of `z` in degrees (duplicates `phiD(z)`).
`static JxnComplexAlgebra`	`asin(JxnComplexAlgebra z)`	Return the inverse sine of `z`.
`static JxnComplexAlgebra`	`asinh(JxnComplexAlgebra z)`	Return the inverse hyperbolic sine of `z`.
`static JxnComplexAlgebra`	`atan(JxnComplexAlgebra z)`	Return the inverse tangent of `z`.
`static JxnComplexAlgebra`	`atanh(JxnComplexAlgebra z)`	Return the inverse hyperbolic tangent of `z`.
`JxnCloneableAlgebra`	`cloneThis()`	Called internally.
`static JxnComplexAlgebra`	`conj(JxnComplexAlgebra z)`	Returns the complex conjugate of `z`.
`static JxnComplexAlgebra`	`cos(JxnComplexAlgebra z)`	Returns the cosine of `z`.
`static JxnComplexAlgebra`	`cosh(JxnComplexAlgebra z)`	Returns the hyperbolic cosine of `z`.
`static JxnComplexAlgebra`	`delta_wye_Z1(JxnComplexAlgebra z12, JxnComplexAlgebra z23, JxnComplexAlgebra z31)`	ΔY-transform: `Z1 = Z12 * Z31 / ( Z12 + Z23 + Z31 )`.
`static JxnComplexAlgebra`	`delta_wye_Z2(JxnComplexAlgebra z12, JxnComplexAlgebra z23, JxnComplexAlgebra z31)`	ΔY-transform: `Z2 = Z23 * Z12 / ( Z12 + Z23 + Z31 )`.
`static JxnComplexAlgebra`	`delta_wye_Z3(JxnComplexAlgebra z12, JxnComplexAlgebra z23, JxnComplexAlgebra z31)`	ΔY-transform: `Z3 = Z31 * Z23 / ( Z12 + Z23 + Z31 )`.
`static JxnComplexAlgebra`	`dif(JxnComplexAlgebra z1, JxnComplexAlgebra z2)`	Returns the difference `z1 - z2`.
`JxnComplexAlgebra`	`div(double d)`	Divides this by `d`.
`JxnComplexAlgebra`	`div(JxnComplexAlgebra z)`	Divides this by `z`.
`JxnComplexArrayAlgebra`	`div(JxnComplexArrayAlgebra ca)`	Returns this divided by `ca`.
`JxnComplexArrayAlgebra`	`div(JxnRealArrayAlgebra ra)`	Returns this divided by `ra`.
`static JxnComplexAlgebra`	`dreieckstern(JxnComplexAlgebra z23, JxnComplexAlgebra z31, JxnComplexAlgebra z12)`	Deprecated. Use `delta_wye_Z1`.
`boolean`	`equals(Object other)`	Complex objects are equal, if both real and imaginary part are equal.
`static JxnComplexAlgebra`	`exp(JxnComplexAlgebra z)`	Returns the exponential function value of `z`.
`static double`	`getEqualityTolerance()`	Returns the tolerance used for the `equals` method.
`static double`	`imag(JxnComplexAlgebra z)`	Returns the imaginary part of `z`.
`JxnComplexAlgebra`	`inv()`	Replaces this by its reciprocal.
`static JxnComplexAlgebra`	`inv(JxnComplexAlgebra z)`	Returns the reciprocal of `z`.
`static JxnComplexAlgebra`	`log(JxnComplexAlgebra z)`	Returns the natural logarithm of `z`.
`static void`	`main(String[] args)`	Test.
`JxnComplexAlgebra`	`mul(double d)`	(Post)Multiplies this by `d`.
`JxnComplexAlgebra`	`mul(JxnComplexAlgebra z)`	(Post)Multiplies this by `z`.
`JxnComplexArrayAlgebra`	`mul(JxnComplexArrayAlgebra ca)`	Returns this (post)multiplied by `ca`.
`JxnComplexArrayAlgebra`	`mul(JxnRealArrayAlgebra ra)`	Returns this (post)multiplied by `ra`.
`static JxnComplexAlgebra`	`parallel(JxnComplexAlgebra z1, JxnComplexAlgebra z2)`	Returns the impedance of the parallel connection of two impedances Z1 und Z2.
`static KmgComplexPhasor`	`phasor(JxnComplexAlgebra z, String label, Color color)`	Returns a phasor representation of `z`.
`static KmgComplexPhasor`	`phasor(JxnComplexAlgebra z0, JxnComplexAlgebra z1, String label, Color color)`	Returns a phasor representation of `z1`.
`static double`	`phi(JxnComplexAlgebra z)`	Returns the argument (phase angle) of `z`.
`static double`	`phiD(JxnComplexAlgebra z)`	Returns the argument (phase angle) of `z` in degrees.
`static JxnComplexPlotFrame`	`plot(JxnComplexAlgebra z)`	See `plot`.
`static JxnComplexPlotFrame`	`plot(JxnComplexAlgebra z, Color color)`	See `plot`.
`static JxnComplexPlotFrame`	`plot(JxnComplexAlgebra z, String label)`	See `plot`.
`static JxnComplexPlotFrame`	`plot(JxnComplexAlgebra z, String label, Color color)`	Creates a new `JxnComplexPlotFrame` and visualizes `z` as a phasor (arrow).
`static JxnComplexPlotFrame`	`plot(JxnComplexAlgebra z0, JxnComplexAlgebra z1)`	See `plot`.
`static JxnComplexPlotFrame`	`plot(JxnComplexAlgebra z0, JxnComplexAlgebra z1, Color color)`	See `plot`.
`static JxnComplexPlotFrame`	`plot(JxnComplexAlgebra z0, JxnComplexAlgebra z1, String label)`	See `plot`.
`static JxnComplexPlotFrame`	`plot(JxnComplexAlgebra z0, JxnComplexAlgebra z1, String label, Color color)`	Creates a new `JxnComplexPlotFrame` and visualizes `z1` as a phasor (arrow).
`static JxnComplexPlotFrame`	`plot90(JxnComplexAlgebra z)`	See `plot90`.
`static JxnComplexPlotFrame`	`plot90(JxnComplexAlgebra z, Color color)`	See `plot90`.
`static JxnComplexPlotFrame`	`plot90(JxnComplexAlgebra z, String label)`	See `plot90`.
`static JxnComplexPlotFrame`	`plot90(JxnComplexAlgebra z, String label, Color color)`	See `plot`.
`static JxnComplexPlotFrame`	`plot90(JxnComplexAlgebra z0, JxnComplexAlgebra z1)`	See `plot90`.
`static JxnComplexPlotFrame`	`plot90(JxnComplexAlgebra z0, JxnComplexAlgebra z1, Color color)`	See `plot90`.
`static JxnComplexPlotFrame`	`plot90(JxnComplexAlgebra z0, JxnComplexAlgebra z1, String label)`	See `plot90`.
`static JxnComplexPlotFrame`	`plot90(JxnComplexAlgebra z0, JxnComplexAlgebra z1, String label, Color color)`	See `plot`.
`JxnComplexAlgebra`	`pow(double d)`	Replaces this by its power of `d`.
`JxnComplexAlgebra`	`pow(JxnComplexAlgebra exponent)`	Replaces this by its power of `exponent`.
`static JxnComplexAlgebra`	`pow(JxnComplexAlgebra z, JxnComplexAlgebra e)`	Returns `z` to the power of `e`.
`JxnComplexArrayAlgebra`	`pow(JxnRealArrayAlgebra ra)`	Returns this by its power of `ra`.
`static JxnComplexAlgebra`	`prd(JxnComplexAlgebra z, double d)`	Returns the product `z * d`.
`static JxnComplexAlgebra`	`prd(JxnComplexAlgebra z1, JxnComplexAlgebra z2)`	Returns the product `z1 * z2`.
`static JxnComplexAlgebra`	`quot(JxnComplexAlgebra z, double d)`	Returns the quotient `z / d`.
`static JxnComplexAlgebra`	`quot(JxnComplexAlgebra z1, JxnComplexAlgebra z2)`	Returns the quotient `z1 / z2`.
`static double`	`real(JxnComplexAlgebra z)`	Returns the real part of `z`.
`static double`	`setEqualityTolerance(double eps)`	Sets the tolerance for the `equals` method for all instances of this class.
`static int`	`setNDec(int nDec)`	Set default decimals for `toString()`.
`static JxnComplexAlgebra`	`sin(JxnComplexAlgebra z)`	Returns the sine of `z`.
`static JxnComplexAlgebra`	`sinh(JxnComplexAlgebra z)`	Returns the hyperbolic sine of `z`.
`static JxnComplexAlgebra`	`sqrt(JxnComplexAlgebra z)`	Returns the square root of `z`.
`static JxnComplexAlgebra`	`sqrt1z(JxnComplexAlgebra z)`	Returns `sqrt( 1 - z * z )`.
`static JxnComplexAlgebra`	`sterndreieck(JxnComplexAlgebra z1, JxnComplexAlgebra z2, JxnComplexAlgebra z3)`	Deprecated. Use `wye_delta_Z23`.
`JxnComplexAlgebra`	`sub(double d)`	Subtracts `d` from this.
`JxnComplexAlgebra`	`sub(JxnComplexAlgebra z)`	Subtracts `z` from this.
`JxnComplexArrayAlgebra`	`sub(JxnComplexArrayAlgebra ca)`	Returns `ca` subtracted from this.
`JxnComplexArrayAlgebra`	`sub(JxnRealArrayAlgebra ra)`	Returns `ra` subtracted from this.
`static JxnComplexAlgebra`	`sum(JxnComplexAlgebra z1, JxnComplexAlgebra z2)`	Returns the sum `z1 + z2`.
`static JxnComplexAlgebra`	`sum(JxnComplexAlgebra z1, JxnComplexAlgebra z2, JxnComplexAlgebra z3)`	Returns the sum `z1 + z2 + z3`.
`static JxnComplexAlgebra`	`tan(JxnComplexAlgebra z)`	Returns the tangent of `z`.
`static JxnComplexAlgebra`	`tanh(JxnComplexAlgebra z)`	Returns the hyperbolic tangent of `z`.
`String`	`toString()`	Formats instance.
`String`	`toString(int nDec)`	Formats instance with `nDec` decimals.
`String`	`toString(int nDec1, int nDec2)`	Formats instance with `nDec1` decimals and `nDec2` decimals for the phase angle.
`static JxnComplexAlgebra`	`wye_delta_Z12(JxnComplexAlgebra z1, JxnComplexAlgebra z2, JxnComplexAlgebra z3)`	YΔ-transform: `Z12 = Z1 + Z2 + Z1 * Z2 / Z3`.
`static JxnComplexAlgebra`	`wye_delta_Z23(JxnComplexAlgebra z1, JxnComplexAlgebra z2, JxnComplexAlgebra z3)`	YΔ-transform: `Z23 = Z2 + Z3 + Z2 * Z3 / Z1`.
`static JxnComplexAlgebra`	`wye_delta_Z31(JxnComplexAlgebra z1, JxnComplexAlgebra z2, JxnComplexAlgebra z3)`	YΔ-transform: `Z31 = Z3 + Z1 + Z3 * Z1 / Z2`.

Methods inherited from class java.lang.Object
clone, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

re
```
public double re
```
Real part.

im
```
public double im
```
Imaginary part.

equalityTolerance
```
protected static double equalityTolerance
```
Tolerance for equals method.

See Also:

setEqualityTolerance(double)

defaultNDec
```
protected static int defaultNDec
```
Default nDec for toString().

See Also:

toString(int)

J

protected static final JxnComplexAlgebra J

j.

ONE

protected static final JxnComplexAlgebra ONE

1 + j 0.

JJJ

protected static final JxnComplexAlgebra JJJ

-j.

Constructor Detail

JxnComplexAlgebra
```
public JxnComplexAlgebra()
```
Creates j.

JxnComplexAlgebra

public JxnComplexAlgebra(JxnComplexAlgebra z)

Creates a copy of z.

JxnComplexAlgebra

public JxnComplexAlgebra(double re)

Creates re + j 0.

JxnComplexAlgebra

public JxnComplexAlgebra(double re,
                         double im)

Creates re + j im.

JxnComplexAlgebra
```
public JxnComplexAlgebra(double r,
                         double phi,
                         boolean deg)
```
Creates complex from magnitude r and phase angle phi.

Parameters:

deg - if true phi is expected in degrees, else in radians

Method Detail

cloneThis
```
public JxnCloneableAlgebra cloneThis()
```
Description copied from interface: JxnCloneableAlgebra

Called internally. Required to avoid overwriting the left side operand opndLeft in opndLeft op opndRght, if op is implemented as opndLeft.op(opndRght) and the instance method op modifies the instance.

Specified by:

cloneThis in interface JxnCloneableAlgebra

Returns:

copy of this instance

equals
```
public boolean equals(Object other)
```
Complex objects are equal, if both real and imaginary part are equal. Use setEqualityTolerance(double) to set a tolerance for the comparision of re and im.

Overrides:

equals in class Object

setEqualityTolerance
```
public static double setEqualityTolerance(double eps)
```
Sets the tolerance for the equals method for all instances of this class.

Parameters:

eps -
eps > 0. absolute difference for re and im
eps < 0. difference relative to the magnitude of the biggest of two instances to be compared

Returns:

old tolerance

getEqualityTolerance
```
public static double getEqualityTolerance()
```
Returns the tolerance used for the equals method.

toString
```
public String toString()
```
Formats instance.

Overrides:

toString in class Object

toString
```
public String toString(int nDec)
```
Formats instance with nDec decimals.

toString
```
public String toString(int nDec1,
                       int nDec2)
```
Formats instance with nDec1 decimals and nDec2 decimals for the phase angle.

setNDec
```
public static int setNDec(int nDec)
```
Set default decimals for toString().

See Also:

toString(int)

add

public JxnComplexAlgebra add(JxnComplexAlgebra z)

Adds z to this.

sub

public JxnComplexAlgebra sub(JxnComplexAlgebra z)

Subtracts z from this.

mul

public JxnComplexAlgebra mul(JxnComplexAlgebra z)

(Post)Multiplies this by z.

div

public JxnComplexAlgebra div(JxnComplexAlgebra z)

Divides this by z.

inv
```
public JxnComplexAlgebra inv()
```
Replaces this by its reciprocal.

pow

public JxnComplexAlgebra pow(JxnComplexAlgebra exponent)

Replaces this by its power of exponent.

add

public JxnComplexAlgebra add(double d)

Adds d to this.

sub

public JxnComplexAlgebra sub(double d)

Subtracts d from this.

mul

public JxnComplexAlgebra mul(double d)

(Post)Multiplies this by d.

div

public JxnComplexAlgebra div(double d)

Divides this by d.

pow
```
public JxnComplexAlgebra pow(double d)
```
Replaces this by its power of d.
Must be implemented, if pow(JxnComplexAlgebra) is not implemented.

add

public JxnComplexArrayAlgebra add(JxnRealArrayAlgebra ra)

Returns ra added to this.

sub

public JxnComplexArrayAlgebra sub(JxnRealArrayAlgebra ra)

Returns ra subtracted from this.

mul

public JxnComplexArrayAlgebra mul(JxnRealArrayAlgebra ra)

Returns this (post)multiplied by ra.

div

public JxnComplexArrayAlgebra div(JxnRealArrayAlgebra ra)

Returns this divided by ra.

pow

public JxnComplexArrayAlgebra pow(JxnRealArrayAlgebra ra)

Returns this by its power of ra.

add

public JxnComplexArrayAlgebra add(JxnComplexArrayAlgebra ca)

Returns ca added to this.

sub

public JxnComplexArrayAlgebra sub(JxnComplexArrayAlgebra ca)

Returns ca subtracted from this.

mul

public JxnComplexArrayAlgebra mul(JxnComplexArrayAlgebra ca)

Returns this (post)multiplied by ca.

div

public JxnComplexArrayAlgebra div(JxnComplexArrayAlgebra ca)

Returns this divided by ca.

inv

public static JxnComplexAlgebra inv(JxnComplexAlgebra z)

Returns the reciprocal of z.

sum

public static JxnComplexAlgebra sum(JxnComplexAlgebra z1,
                                    JxnComplexAlgebra z2)

Returns the sum z1 + z2.

sum

public static JxnComplexAlgebra sum(JxnComplexAlgebra z1,
                                    JxnComplexAlgebra z2,
                                    JxnComplexAlgebra z3)

Returns the sum z1 + z2 + z3.

dif

public static JxnComplexAlgebra dif(JxnComplexAlgebra z1,
                                    JxnComplexAlgebra z2)

Returns the difference z1 - z2.

prd

public static JxnComplexAlgebra prd(JxnComplexAlgebra z1,
                                    JxnComplexAlgebra z2)

Returns the product z1 * z2.

quot

public static JxnComplexAlgebra quot(JxnComplexAlgebra z1,
                                     JxnComplexAlgebra z2)

Returns the quotient z1 / z2.

prd

public static JxnComplexAlgebra prd(JxnComplexAlgebra z,
                                    double d)

Returns the product z * d.

quot

public static JxnComplexAlgebra quot(JxnComplexAlgebra z,
                                     double d)

Returns the quotient z / d.

abs
```
public static double abs(JxnComplexAlgebra z)
```
Returns the absolute value (magnitude) of z. abs( re + j im ) ≡ Math.hypot( re, im ) ≡ sqrt( re * re + im * im ).

phi
```
public static double phi(JxnComplexAlgebra z)
```
Returns the argument (phase angle) of z. phi( re + j im ) ≡ Math.atan2( im, re ).

arg
```
public static double arg(JxnComplexAlgebra z)
```
Returns the argument (phase angle) of z (duplicates phi(z)).

phiD
```
public static double phiD(JxnComplexAlgebra z)
```
Returns the argument (phase angle) of z in degrees. phiD(z) ≡ phi(z) * 180. / PI.

argD
```
public static double argD(JxnComplexAlgebra z)
```
Returns the argument (phase angle) of z in degrees (duplicates phiD(z)).

real

public static double real(JxnComplexAlgebra z)

Returns the real part of z.

imag

public static double imag(JxnComplexAlgebra z)

Returns the imaginary part of z.

conj
```
public static JxnComplexAlgebra conj(JxnComplexAlgebra z)
```
Returns the complex conjugate of z. conj( re + j im ) ≡ ( re - j im ).

sqrt
```
public static JxnComplexAlgebra sqrt(JxnComplexAlgebra z)
```
Returns the square root of z. sqrt(z) ≡ Math.sqrt( abs(z) ) * exp( j 0.5 arg(z) ).

exp
```
public static JxnComplexAlgebra exp(JxnComplexAlgebra z)
```
Returns the exponential function value of z. exp( re + j im ) ≡ Math.exp(re) * ( Math.cos(im) + j Math.sin(im) ).

log
```
public static JxnComplexAlgebra log(JxnComplexAlgebra z)
```
Returns the natural logarithm of z. log(z) ≡ Math.log( abs(z) ) + j arg(z).

pow

public static JxnComplexAlgebra pow(JxnComplexAlgebra z,
                                    JxnComplexAlgebra e)

Returns z to the power of e. pow(z,e) ≡ exp( e * log(z) ).

sinh
```
public static JxnComplexAlgebra sinh(JxnComplexAlgebra z)
```
Returns the hyperbolic sine of z. sinh(z) ≡ ( exp(z) - exp(-z) ) / 2.

cosh
```
public static JxnComplexAlgebra cosh(JxnComplexAlgebra z)
```
Returns the hyperbolic cosine of z. cosh(z) ≡ ( exp(z) + exp(-z) ) / 2.

tanh
```
public static JxnComplexAlgebra tanh(JxnComplexAlgebra z)
```
Returns the hyperbolic tangent of z. tanh(z) ≡ ( exp(z) - exp(-z) ) / ( exp(z) + exp(-z) ).

asinh
```
public static JxnComplexAlgebra asinh(JxnComplexAlgebra z)
```
Return the inverse hyperbolic sine of z. asinh(z) ≡ log( z + sqrt( z * z + 1 ) ).

See Also:

Wikipedia

acosh
```
public static JxnComplexAlgebra acosh(JxnComplexAlgebra z)
```
Return the inverse hyperbolic cosine of z. acosh(z) ≡ log( z + sqrt( z + 1 ) * sqrt( z - 1 ) ).

See Also:

Wikipedia

atanh
```
public static JxnComplexAlgebra atanh(JxnComplexAlgebra z)
```
Return the inverse hyperbolic tangent of z. atanh(z) ≡ log( ( 1 + z )/( 1 - z ) ) / 2.

See Also:

Wikipedia

sin

public static JxnComplexAlgebra sin(JxnComplexAlgebra z)

Returns the sine of z. sin(z) ≡ -j sinh( j z ).

cos

public static JxnComplexAlgebra cos(JxnComplexAlgebra z)

Returns the cosine of z. cos(z) ≡ cosh( j z ).

tan

public static JxnComplexAlgebra tan(JxnComplexAlgebra z)

Returns the tangent of z. tan(z) ≡ -j tanh( j z ).

sqrt1z

public static JxnComplexAlgebra sqrt1z(JxnComplexAlgebra z)

Returns sqrt( 1 - z * z ).

asin
```
public static JxnComplexAlgebra asin(JxnComplexAlgebra z)
```
Return the inverse sine of z. asin(z) ≡ -j log( j z + sqrt( 1 - z * z ) ).

See Also:

Wikipedia

acos
```
public static JxnComplexAlgebra acos(JxnComplexAlgebra z)
```
Return the inverse cosine of z. acos(z) ≡ -j log( z + j sqrt( 1 - z * z ) ).

See Also:

Wikipedia

atan
```
public static JxnComplexAlgebra atan(JxnComplexAlgebra z)
```
Return the inverse tangent of z. atan(z) ≡ j log( ( j + z )/( j - z ) ) / 2.

See Also:

Wikipedia

parallel

public static JxnComplexAlgebra parallel(JxnComplexAlgebra z1,
                                         JxnComplexAlgebra z2)

Returns the impedance of the parallel connection of two impedances Z1 und Z2. Zp = Z1 * Z2 / ( Z1 + Z2 ).

dreieckstern

public static JxnComplexAlgebra dreieckstern(JxnComplexAlgebra z23,
                                             JxnComplexAlgebra z31,
                                             JxnComplexAlgebra z12)

Deprecated.

Use delta_wye_Z1. Umwandlung Dreieck -> Stern: Berechnet Z₁( Z₂₃, Z₃₁, Z₁₂ ).

sterndreieck

public static JxnComplexAlgebra sterndreieck(JxnComplexAlgebra z1,
                                             JxnComplexAlgebra z2,
                                             JxnComplexAlgebra z3)

Deprecated.

Use wye_delta_Z23. Umwandlung Stern -> Dreieck: Berechnet Z₂₃( Z₁, Z₂, Z₃ ).

delta_wye_Z1

public static JxnComplexAlgebra delta_wye_Z1(JxnComplexAlgebra z12,
                                             JxnComplexAlgebra z23,
                                             JxnComplexAlgebra z31)

ΔY-transform: Z1 = Z12 * Z31 / ( Z12 + Z23 + Z31 ).

See Also:: Wikipedia

delta_wye_Z2

public static JxnComplexAlgebra delta_wye_Z2(JxnComplexAlgebra z12,
                                             JxnComplexAlgebra z23,
                                             JxnComplexAlgebra z31)

ΔY-transform: Z2 = Z23 * Z12 / ( Z12 + Z23 + Z31 ).

See Also:: Wikipedia

delta_wye_Z3

public static JxnComplexAlgebra delta_wye_Z3(JxnComplexAlgebra z12,
                                             JxnComplexAlgebra z23,
                                             JxnComplexAlgebra z31)

ΔY-transform: Z3 = Z31 * Z23 / ( Z12 + Z23 + Z31 ).

See Also:: Wikipedia

wye_delta_Z12

public static JxnComplexAlgebra wye_delta_Z12(JxnComplexAlgebra z1,
                                              JxnComplexAlgebra z2,
                                              JxnComplexAlgebra z3)

YΔ-transform: Z12 = Z1 + Z2 + Z1 * Z2 / Z3.

See Also:: Wikipedia

wye_delta_Z23

public static JxnComplexAlgebra wye_delta_Z23(JxnComplexAlgebra z1,
                                              JxnComplexAlgebra z2,
                                              JxnComplexAlgebra z3)

YΔ-transform: Z23 = Z2 + Z3 + Z2 * Z3 / Z1.

See Also:: Wikipedia

wye_delta_Z31

public static JxnComplexAlgebra wye_delta_Z31(JxnComplexAlgebra z1,
                                              JxnComplexAlgebra z2,
                                              JxnComplexAlgebra z3)

YΔ-transform: Z31 = Z3 + Z1 + Z3 * Z1 / Z2.

See Also:: Wikipedia

plot
```
public static JxnComplexPlotFrame plot(JxnComplexAlgebra z,
                                       String label,
                                       Color color)
```
Creates a new JxnComplexPlotFrame and visualizes z as a phasor (arrow).
Call the add and apnd methods on the JxnComplexPlotFrame instance returned by this method to display further phasors in the same PlotFrame.

Returns:

PlotFrame instance can be used to add further phasors and curves.

See Also:

JxnComplexPlotFrame, JXN Tutorial

plot

public static JxnComplexPlotFrame plot(JxnComplexAlgebra z,
                                       String label)

See plot.

plot

public static JxnComplexPlotFrame plot(JxnComplexAlgebra z,
                                       Color color)

See plot.

plot

public static JxnComplexPlotFrame plot(JxnComplexAlgebra z)

See plot.

plot

public static JxnComplexPlotFrame plot(JxnComplexAlgebra z0,
                                       JxnComplexAlgebra z1,
                                       String label,
                                       Color color)

Creates a new JxnComplexPlotFrame and visualizes z1 as a phasor (arrow). The starting point of the arrow is given by z0.
See also plot.

plot

public static JxnComplexPlotFrame plot(JxnComplexAlgebra z0,
                                       JxnComplexAlgebra z1,
                                       String label)

See plot.

plot

public static JxnComplexPlotFrame plot(JxnComplexAlgebra z0,
                                       JxnComplexAlgebra z1,
                                       Color color)

See plot.

plot

public static JxnComplexPlotFrame plot(JxnComplexAlgebra z0,
                                       JxnComplexAlgebra z1)

See plot.

plot90

public static JxnComplexPlotFrame plot90(JxnComplexAlgebra z,
                                         String label,
                                         Color color)

See plot. Orientation of the coordinate system: real axis points up.

plot90

public static JxnComplexPlotFrame plot90(JxnComplexAlgebra z,
                                         String label)

See plot90.

plot90

public static JxnComplexPlotFrame plot90(JxnComplexAlgebra z,
                                         Color color)

See plot90.

plot90

public static JxnComplexPlotFrame plot90(JxnComplexAlgebra z)

See plot90.

plot90

public static JxnComplexPlotFrame plot90(JxnComplexAlgebra z0,
                                         JxnComplexAlgebra z1,
                                         String label,
                                         Color color)

See plot. Orientation of the coordinate system: real axis points up.

plot90

public static JxnComplexPlotFrame plot90(JxnComplexAlgebra z0,
                                         JxnComplexAlgebra z1,
                                         String label)

See plot90.

plot90

public static JxnComplexPlotFrame plot90(JxnComplexAlgebra z0,
                                         JxnComplexAlgebra z1,
                                         Color color)

See plot90.

plot90

public static JxnComplexPlotFrame plot90(JxnComplexAlgebra z0,
                                         JxnComplexAlgebra z1)

See plot90.

phasor
```
public static KmgComplexPhasor phasor(JxnComplexAlgebra z,
                                      String label,
                                      Color color)
```
Returns a phasor representation of z. Call the add method on a PlotFrame instance to display the phasor in the PlotFrame. Allows e.g. to show a phasor in a JxnRealArrayPlotFrame.

Note: Please do not apply add( phasor( z, label, color ) ) together with any of the plot90(...) methods. With plot90 directly use add: plot90(...).add( z, label, color ).

phasor
```
public static KmgComplexPhasor phasor(JxnComplexAlgebra z0,
                                      JxnComplexAlgebra z1,
                                      String label,
                                      Color color)
```
Returns a phasor representation of z1. The starting point of the arrow is given by z0. Call the add method on a PlotFrame instance to display the phasor in the PlotFrame. Allows e.g. to show a phasor in a JxnRealArrayPlotFrame.

Note: Please do not apply add( phasor( z0, z1, label, color ) ) together with any of the plot90(...) methods. With plot90 directly use add: plot90(...).add( z0, z1, label, color ).

angle
```
public static KmgComplexAngle angle(JxnComplexAlgebra center,
                                    JxnComplexAlgebra phiStart,
                                    JxnComplexAlgebra phiTip,
                                    double radFak,
                                    String label,
                                    Color color)
```
Returns an angle (arc with arrow tip). Call the add method on a PlotFrame instance to display the angle in the PlotFrame.

Parameters:

center - complex representing the center of the arc

phiStart - phi(phiStart) defines the start angle of the arc (related to the real axis)

phiTip - phi(phiTip) defines the end angle of the arc (related to the real axis)

radFak - determines the radius of the arc:
> 0 the radius of the arc is radFak * min( abs(phiStart), abs(phiTip) )
< 0 the radius of the arc is radFak
= 0 the radius of the arc is 0.9 * min( abs(phiStart), abs(phiTip) )

angle

public static KmgComplexAngle angle(JxnComplexAlgebra center,
                                    JxnComplexAlgebra phiStart,
                                    JxnComplexAlgebra phiTip,
                                    double radFak,
                                    String label,
                                    Color color,
                                    boolean d90)

See angle.

Parameters:: d90 - the orientation of the coordinate system: true ⇒ real axis points up, false ⇒ real axis points right

angle

public static KmgComplexAngle angle(JxnComplexAlgebra phiStart,
                                    JxnComplexAlgebra phiTip,
                                    double radFak,
                                    String label,
                                    Color color)

See angle. The center of the arc is (0,0).

angle

public static KmgComplexAngle angle(JxnComplexAlgebra phiStart,
                                    JxnComplexAlgebra phiTip,
                                    double radFak,
                                    String label,
                                    Color color,
                                    boolean d90)

See angle. The center of the arc is (0,0).

Parameters:: d90 - the orientation of the coordinate system: true ⇒ real axis points up, false ⇒ real axis points right

angle

public static KmgComplexAngle angle(JxnComplexAlgebra center,
                                    double radius,
                                    double startAngle,
                                    double tipAngle,
                                    String label,
                                    Color color)

See angle.

Parameters:: radius - radius of the arc; startAngle - start angle of the arc (related to the real axis); tipAngle - end angle of the arc (related to the real axis)

angle

public static KmgComplexAngle angle(JxnComplexAlgebra center,
                                    double radius,
                                    double startAngle,
                                    double tipAngle,
                                    String label,
                                    Color color,
                                    boolean d90)

See angle.

Parameters:: d90 - the orientation of the coordinate system: true ⇒ real axis points up, false ⇒ real axis points right

main

public static void main(String[] args)

Test.

Class JxnComplexAlgebra

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

re

im

equalityTolerance

defaultNDec

J

ONE

JJJ

Constructor Detail

JxnComplexAlgebra

JxnComplexAlgebra

JxnComplexAlgebra

JxnComplexAlgebra

JxnComplexAlgebra

Method Detail

cloneThis

equals

setEqualityTolerance

getEqualityTolerance

toString

toString

toString

setNDec

add

sub

mul

div

inv

pow

add

sub

mul

div

pow

add

sub

mul

div

pow

add

sub

mul

div

inv

sum

sum

dif

prd

quot

prd

quot

abs

phi

arg

phiD

argD

real

imag

conj

sqrt

exp

log

pow

sinh

cosh

tanh

asinh

acosh

atanh

sin

cos

tan

sqrt1z

asin

acos