Complex

Complex number with overloaded operators

Information

Complex number defined as a record containing real and imaginary part, utilizing operator overloading.

Licensed by the Modelica Association under the 3-Clause BSD License
Copyright © 2010-2025, Modelica Association and contributors

This Modelica package is free software and the use is completely at your own risk; it can be redistributed and/or modified under the terms of the 3-Clause BSD license. For license conditions (including the disclaimer of warranty) visit https://modelica.org/licenses/modelica-3-clause-bsd.

Contents

Package Content

Name	Description
'constructor'	Constructor
'0'	Zero-element of addition (= Complex(0))
'-'	Unary and binary minus
'*'	Multiplication
'+'	Add two complex numbers
'/'	Divide two complex numbers
'^'	Power
'=='	Test whether two complex numbers are identical
'<>'	Test whether two complex numbers are not identical
'String'	Transform Complex number into a String representation

Complex.'constructor'

Constructor

Information

Here the constructor operator(s) is/are defined.

Package Content

Name	Description
fromReal	Construct Complex from Real

Complex.'constructor'.fromReal

Construct Complex from Real

Information

This function returns a Complex number defined by real part re and optional imaginary part im (default=0).

Inputs

Outputs

Complex.'0'

Zero-element of addition (= Complex(0))

Information

This function returns the zero-element of Complex, that is, Complex(0) = 0 + j*0.

Outputs

Complex.'-'

Unary and binary minus

Information

Here the unary and binary minus operator(s) is/are defined.

Package Content

Name	Description
negate	Unary minus (multiply complex number by -1)
subtract	Subtract two complex numbers

Complex.'-'.negate

Unary minus (multiply complex number by -1)

Information

This function returns the binary minus of the given Complex number.

Inputs

Outputs

Complex.'-'.subtract

Subtract two complex numbers

Information

This function returns the difference of two given Complex numbers.

Inputs

Outputs

Complex.'*'

Multiplication

Information

Here the multiplication operator(s) is/are defined.

Package Content

Name	Description
multiply	Multiply two complex numbers
scalarProduct	Scalar product of two complex vectors c1 and c2

Complex.'*'.multiply

Multiply two complex numbers

Information

This function returns the product of two given Complex numbers.

Inputs

Outputs

Complex.'*'.scalarProduct

Scalar product of two complex vectors c1 and c2

Information

This function returns the scalar product of two given vectors of Complex numbers of length n.

c3 = sum(conj(c1[k]) * c2[k] for k in 1:n)

Inputs

Outputs

Complex.'+'

Add two complex numbers

Information

This function returns the sum of two given Complex numbers.

Inputs

Outputs

Complex.'/'

Divide two complex numbers

Information

This function returns the quotient of two given Complex numbers.

Inputs

Outputs

Complex.'^'

Power

Package Content

Name	Description
complexPower	Complex power of complex number
integerPower	Integer power of complex number

Complex.'^'.complexPower

Complex power of complex number

Information

This function returns the given Complex number c1 to the power of the Complex number c2.

Inputs

Outputs

Complex.'^'.integerPower

Integer power of complex number

Information

This function returns the given Complex number c1 to the power of the Integer number c2.

This also works for zero exponent.

Inputs

Outputs

Complex.'=='

Test whether two complex numbers are identical

Information

This function tests whether two given Complex numbers are equal.

Inputs

Outputs

Complex.'<>'

Test whether two complex numbers are not identical

Information

This function tests whether two given Complex numbers are not equal.

Inputs

Outputs

Complex.'String'

Transform Complex number into a String representation

Information

This function converts a given Complex number to String representation.

Inputs

Outputs