# Package Modelica.​ComplexMathLibrary of complex mathematical functions (e.g., sin, cos) and of functions operating on complex vectors and matrices

### Information

This package contains basic mathematical functions operating on complex numbers (such as sin(..)), as well as functions operating on vectors of complex numbers.

Extends from `Modelica.​Icons.​Package` (Icon for standard packages).

### Package Contents

NameDescription
`'abs'`Absolute value of complex number
`'max'`Return maximum element of complex vector
`'min'`Return minimum element of complex vector
`'product'`Return product of complex vector
`'sqrt'`Square root of complex number
`'sum'`Return sum of complex vector
`acos`Arc-cosine of complex number
`acosh`Area-hyperbolic-cosine of complex number
`arg`Phase angle of complex number
`asin`Arc-sine of complex number
`asinh`Area-hyperbolic-sine of complex number
`atan`Arc-tangent of complex number
`atanh`Area-hyperbolic-tangent of complex number
`conj`Conjugate of complex number
`cos`Cosine of complex number
`cosh`Hyperbolic-cosine of complex number
`exp`Exponential of complex number
`fromPolar`Complex from polar representation
`imag`Imaginary part of complex number
`log`Logarithm of complex number
`real`Real part of complex number
`sin`Sine of complex number
`sinh`Hyperbolic-sine of complex number
`tan`Tangent of complex number
`tanh`Hyperbolic-tangent of complex number
`Vectors`Library of functions operating on complex vectors

### Package Constants

TypeNameValueDescription
`final ``Complex``j``Complex(0, 1)`Imaginary unit

## Function Modelica.​ComplexMath.​sinSine of complex number

### Information

This function returns the Complex sine of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`sin(c1)

## Function Modelica.​ComplexMath.​cosCosine of complex number

### Information

This function returns the Complex cosine of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= cos(c1)

## Function Modelica.​ComplexMath.​tanTangent of complex number

### Information

This function returns the Complex tangent of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= tan(c1)

## Function Modelica.​ComplexMath.​asinArc-sine of complex number

### Information

This function returns the inverse Complex sine of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`arc_sin(c1)

## Function Modelica.​ComplexMath.​acosArc-cosine of complex number

### Information

This function returns the inverse Complex cosine of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= arc_cos(c1)

## Function Modelica.​ComplexMath.​atanArc-tangent of complex number

### Information

This function returns the inverse Complex tangent of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= arc_tan(c1)

## Function Modelica.​ComplexMath.​sinhHyperbolic-sine of complex number

### Information

This function returns the Complex hyperbolic sine of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`sinh(c1)

## Function Modelica.​ComplexMath.​coshHyperbolic-cosine of complex number

### Information

This function returns the Complex hyperbolic cosine of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= cosh(c1)

## Function Modelica.​ComplexMath.​tanhHyperbolic-tangent of complex number

### Information

This function returns the Complex hyperbolic tangent of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= tanh(c1)

## Function Modelica.​ComplexMath.​asinhArea-hyperbolic-sine of complex number

### Information

This function returns the inverse Complex hyperbolic sine of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`ar_sinh(c1)

## Function Modelica.​ComplexMath.​acoshArea-hyperbolic-cosine of complex number

### Information

This function returns the inverse Complex hyperbolic cosine of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= ar_cosh(c1)

## Function Modelica.​ComplexMath.​atanhArea-hyperbolic-tangent of complex number

### Information

This function returns the inverse Complex hyperbolic tangent of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= ar_tanh(c1)

## Function Modelica.​ComplexMath.​expExponential of complex number

### Information

This function returns the Complex natural exponential of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= exp(c1)

## Function Modelica.​ComplexMath.​logLogarithm of complex number

### Information

This function returns the Complex natural logarithm of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= log(c1)

## Function Modelica.​ComplexMath.​'abs'Absolute value of complex number

### Information

This function returns the Real absolute of the Complex input, i.e., its length.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c`Complex number

### Outputs

TypeNameDescription
`Real``result`= abs(c)

## Function Modelica.​ComplexMath.​argPhase angle of complex number

### Information

This function returns the Real argument of the Complex input, i.e., its angle.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c`Complex number
`Angle``phi0`Phase angle phi shall be in the range: -pi < phi-phi0 < pi

### Outputs

TypeNameDescription
`Angle``phi`= phase angle of c

## Function Modelica.​ComplexMath.​conjConjugate of complex number

### Information

This function returns the Complex conjugate of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= c1.re - j*c1.im

## Function Modelica.​ComplexMath.​realReal part of complex number

### Information

This function returns the real part of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c`Complex number

### Outputs

TypeNameDescription
`Real``r`= c.re

## Function Modelica.​ComplexMath.​imagImaginary part of complex number

### Information

This function returns the imaginary part of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c`Complex number

### Outputs

TypeNameDescription
`Real``r`= c.im

## Function Modelica.​ComplexMath.​fromPolarComplex from polar representation

### Information

This function constructs a Complex number from its length (absolute) and angle (argument).

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Real``len`abs of complex
`Angle``phi`arg of complex

### Outputs

TypeNameDescription
`Complex``c`= len*cos(phi) + j*len*sin(phi)

## Function Modelica.​ComplexMath.​'sqrt'Square root of complex number

### Information

This function returns the Complex square root (principal square root) of the Complex input.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``c1`Complex number

### Outputs

TypeNameDescription
`Complex``c2`= sqrt(c1)

## Function Modelica.​ComplexMath.​'max'Return maximum element of complex vector

### Information

This function returns the largest element of the Complex input vector, defined by the Complex absolute.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``v[:]`Vector

### Outputs

TypeNameDescription
`Complex``result`Element of v with largest absolute value
`Integer``index`v[index] has the largest absolute value

## Function Modelica.​ComplexMath.​'min'Return minimum element of complex vector

### Information

This function returns the smallest element of the Complex input vector, defined by the Complex absolute.

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``v[:]`Vector

### Outputs

TypeNameDescription
`Complex``result`Element of v with smallest absolute value
`Integer``index`v[index] has the smallest absolute value

## Function Modelica.​ComplexMath.​'sum'Return sum of complex vector

### Information

This function returns the Complex sum of the Complex input vector

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``v[:]`Vector

### Outputs

TypeNameDescription
`Complex``result`Complex sum of vector elements

## Function Modelica.​ComplexMath.​'product'Return product of complex vector

### Information

This function returns the Complex product of the Complex input vector

Extends from `Modelica.​Icons.​Function` (Icon for functions).

### Inputs

TypeNameDescription
`Complex``v[:]`Vector

### Outputs

TypeNameDescription
`Complex``result`Complex product of vector elements