etomica.math

## Class Complex

• java.lang.Object
• etomica.math.Complex

• ```public class Complex
extends java.lang.Object```
handle complex variables and relevant operations from Internet
• ### Constructor Summary

Constructors
Constructor and Description
```Complex(double u, double v)```
Constructs the complex number z = u + i*v
• ### Method Summary

All Methods
Modifier and Type Method and Description
`double` `arg()`
Argument of this Complex number, the angle in radians with the x-axis in polar coordinates.
`Complex` `chs()`
Negative of this complex number (chs stands for change sign).
`Complex` `conjugate()`
Complex conjugate of this Complex number (the conjugate of x+i*y is x-i*y).
`Complex` `cos()`
Cosine of this Complex number (doesn't change this Complex number).
`Complex` `cosh()`
Hyperbolic cosine of this Complex number (doesn't change this Complex number).
`Complex` `div(Complex w)`
Division of Complex numbers (doesn't change this Complex number).
`Complex` `exponential()`
Complex exponential (doesn't change this Complex number).
`double` `imagine()`
Imaginary part of this Complex number,the y-coordinate in rectangular coordinates.
`Complex` `log()`
Principal branch of the Complex logarithm of this Complex number.
`Complex` `minus(Complex w)`
Subtraction of Complex numbers (doesn't change this Complex number).
`double` `modulus()`
Modulus of this Complex number, the distance from the origin in polar coordinates.
`Complex` `plus(Complex w)`
Addition of Complex numbers (doesn't change this Complex number).
`double` `real()`
Real part of this Complex number, the x-coordinate in rectangular coordinates.return Re[z] where z is this Complex number.
`Complex` `sin()`
Sine of this Complex number (doesn't change this Complex number).
`Complex` `sinh()`
Hyperbolic sine of this Complex number (doesn't change this Complex number).
`Complex` `sqrt()`
Complex square root (doesn't change this complex number).
`Complex` `tan()`
Tangent of this Complex number (doesn't change this Complex number).
`Complex` `times(Complex w)`
Complex multiplication (doesn't change this Complex number).
`java.lang.String` `toString()`
String representation of this Complex number.
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait`
• ### Constructor Detail

• #### Complex

```public Complex(double u,
double v)```
Constructs the complex number z = u + i*v
Parameters:
`u` - Real part
`v` - Imaginary part
• ### Method Detail

• #### real

`public double real()`
Real part of this Complex number, the x-coordinate in rectangular coordinates.return Re[z] where z is this Complex number.
• #### imagine

`public double imagine()`
Imaginary part of this Complex number,the y-coordinate in rectangular coordinates.
Returns:
Im[z] where z is this Complex number.
• #### modulus

`public double modulus()`
Modulus of this Complex number, the distance from the origin in polar coordinates.
Returns:
|z| where z is this Complex number.
• #### arg

`public double arg()`
Argument of this Complex number, the angle in radians with the x-axis in polar coordinates. The argument or phase of z is the angle of the radius with the positive real axis, and is written as arg(z)
Returns:
arg(z) where z is this Complex number.
• #### conjugate

`public Complex conjugate()`
Complex conjugate of this Complex number (the conjugate of x+i*y is x-i*y).
Returns:
z-bar where z is this Complex number.
• #### plus

`public Complex plus(Complex w)`
Addition of Complex numbers (doesn't change this Complex number).
(x+i*y) + (s+i*t) = (x+s)+i*(y+t).
Parameters:
`w` - is the number to add.
Returns:
z+w where z is this Complex number.
• #### minus

`public Complex minus(Complex w)`
Subtraction of Complex numbers (doesn't change this Complex number).
Parameters:
`w` - is the number to subtract.
Returns:
z-w where z is this Complex number.
• #### times

`public Complex times(Complex w)`
Complex multiplication (doesn't change this Complex number).
Parameters:
`w` - is the number to multiply by.
Returns:
z*w where z is this Complex number.
• #### div

`public Complex div(Complex w)`
Division of Complex numbers (doesn't change this Complex number). (x+i*y)/(s+i*t) = ((x*s+y*t) + i*(y*s-y*t)) / (s^2+t^2)
Parameters:
`w` - is the number to divide by
Returns:
new Complex number z/w where z is this Complex number
• #### exponential

`public Complex exponential()`
Complex exponential (doesn't change this Complex number).
Returns:
exp(z) where z is this Complex number.
• #### log

`public Complex log()`
Principal branch of the Complex logarithm of this Complex number. (doesn't change this Complex number). The principal branch is the branch with -pi < arg <= pi.
Returns:
log(z) where z is this Complex number.
• #### sqrt

`public Complex sqrt()`
Complex square root (doesn't change this complex number). Computes the principal branch of the square root, which is the value with 0 <= arg < pi.
Returns:
sqrt(z) where z is this Complex number.
• #### sin

`public Complex sin()`
Sine of this Complex number (doesn't change this Complex number). sin(z) = (exp(i*z)-exp(-i*z))/(2*i).
Returns:
sin(z) where z is this Complex number.
• #### cos

`public Complex cos()`
Cosine of this Complex number (doesn't change this Complex number). cos(z) = (exp(i*z)+exp(-i*z))/ 2.
Returns:
cos(z) where z is this Complex number.
• #### sinh

`public Complex sinh()`
Hyperbolic sine of this Complex number (doesn't change this Complex number). sinh(z) = (exp(z)-exp(-z))/2.
Returns:
sinh(z) where z is this Complex number.
• #### cosh

`public Complex cosh()`
Hyperbolic cosine of this Complex number (doesn't change this Complex number). cosh(z) = (exp(z) + exp(-z)) / 2.
Returns:
cosh(z) where z is this Complex number.
• #### tan

`public Complex tan()`
Tangent of this Complex number (doesn't change this Complex number). tan(z) = sin(z)/cos(z).
Returns:
tan(z) where z is this Complex number.
• #### chs

`public Complex chs()`
Negative of this complex number (chs stands for change sign). This produces a new Complex number and doesn't change this Complex number.
-(x+i*y) = -x-i*y.
Returns:
-z where z is this Complex number.
• #### toString

`public java.lang.String toString()`
String representation of this Complex number.
Overrides:
`toString` in class `java.lang.Object`
Returns:
x+i*y, x-i*y, x, or i*y as appropriate.