## Modelica.ComplexMath

Library 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 Content

Name Description
j=Complex(0, 1) Imaginary unit
Vectors Library of functions operating on complex vectors
sin Sine of complex number
cos Cosine of complex number
tan Tangent of complex number
asin Arc-sine of complex number
acos Arc-cosine of complex number
atan Arc-tangent of complex number
sinh Hyperbolic-sine of complex number
cosh Hyperbolic-cosine of complex number
tanh Hyperbolic-tangent of complex number
asinh Area-hyperbolic-sine of complex number
acosh Area-hyperbolic-cosine of complex number
atanh Area-hyperbolic-tangent of complex number
exp Exponential of complex number
log Logarithm of complex number
'abs' Absolute value of complex number
arg Phase angle of complex number
conj Conjugate of complex number
real Real part of complex number
imag Imaginary part of complex number
fromPolar Complex from polar representation
'sqrt' Square root of complex number
'max' Return maximum element of complex vector
'min' Return minimum element of complex vector
'sum' Return sum of complex vector
'product' Return product of complex vector

## Modelica.ComplexMath.sin

Sine of complex number

### Information

This function returns the Complex sine of the Complex input.

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

NameDescription
c1Complex number

NameDescription
c2sin(c1)

## Modelica.ComplexMath.cos

Cosine of complex number

### Information

This function returns the Complex cosine of the Complex input.

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

NameDescription
c1Complex number

NameDescription
c2= cos(c1)

## Modelica.ComplexMath.tan

Tangent of complex number

### Information

This function returns the Complex tangent of the Complex input.

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

NameDescription
c1Complex number

NameDescription
c2= tan(c1)

## Modelica.ComplexMath.asin

Arc-sine of complex number

### Information

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

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

NameDescription
c1Complex number

NameDescription
c2arc_sin(c1)

## Modelica.ComplexMath.acos

Arc-cosine of complex number

### Information

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

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

NameDescription
c1Complex number

NameDescription
c2= arc_cos(c1)

## Modelica.ComplexMath.atan

Arc-tangent of complex number

### Information

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

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

NameDescription
c1Complex number

NameDescription
c2= arc_tan(c1)

## Modelica.ComplexMath.sinh

Hyperbolic-sine of complex number

### Information

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

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

NameDescription
c1Complex number

NameDescription
c2sinh(c1)

## Modelica.ComplexMath.cosh

Hyperbolic-cosine of complex number

### Information

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

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

NameDescription
c1Complex number

NameDescription
c2= cosh(c1)

## Modelica.ComplexMath.tanh

Hyperbolic-tangent of complex number

### Information

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

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

NameDescription
c1Complex number

NameDescription
c2= tanh(c1)

## Modelica.ComplexMath.asinh

Area-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).

NameDescription
c1Complex number

NameDescription
c2ar_sinh(c1)

## Modelica.ComplexMath.acosh

Area-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).

NameDescription
c1Complex number

NameDescription
c2= ar_cosh(c1)

## Modelica.ComplexMath.atanh

Area-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).

NameDescription
c1Complex number

NameDescription
c2= ar_tanh(c1)

## Modelica.ComplexMath.exp

Exponential of complex number

### Information

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

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

NameDescription
c1Complex number

NameDescription
c2= exp(c1)

## Modelica.ComplexMath.log

Logarithm of complex number

### Information

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

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

NameDescription
c1Complex number

NameDescription
c2= log(c1)

## 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).

NameDescription
cComplex number

NameDescription
result= abs(c)

## Modelica.ComplexMath.arg

Phase 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

NameDescription
cComplex number
phi0Phase angle phi shall be in the range: -pi < phi-phi0 < pi [rad]

### Outputs

NameDescription
phi= phase angle of c [rad]

## Modelica.ComplexMath.conj

Conjugate of complex number

### Information

This function returns the Complex conjugate of the Complex input.

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

NameDescription
c1Complex number

### Outputs

NameDescription
c2= c1.re - j*c1.im

## Modelica.ComplexMath.real

Real part of complex number

### Information

This function returns the real part of the Complex input.

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

NameDescription
cComplex number

NameDescription
r= c.re

## Modelica.ComplexMath.imag

Imaginary part of complex number

### Information

This function returns the imaginary part of the Complex input.

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

NameDescription
cComplex number

NameDescription
r= c.im

## Modelica.ComplexMath.fromPolar

Complex 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

NameDescription
lenabs of complex
phiarg of complex [rad]

### Outputs

NameDescription
c= len*cos(phi) + j*len*sin(phi)

## 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).

NameDescription
c1Complex number

NameDescription
c2= sqrt(c1)

## 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).

NameDescription
v[:]Vector

### Outputs

NameDescription
resultElement of v with largest absolute value
indexv[index] has the largest absolute value

## 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).

NameDescription
v[:]Vector

### Outputs

NameDescription
resultElement of v with smallest absolute value
indexv[index] has the smallest absolute value

## 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).

NameDescription
v[:]Vector

### Outputs

NameDescription
resultComplex sum of vector elements

## 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).

NameDescription
v[:]Vector

### Outputs

NameDescription
resultComplex product of vector elements
Automatically generated Mon Oct 1 14:51:23 2018.