Complex Structure

Complex Structure

Set of mathematical functions for complex numbers. It provides the basic operations (addition, subtraction, multiplication, division) as well as a set of complex functions.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

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[SerializableAttribute]
public struct Complex : IComparable, IFormattable

<SerializableAttribute>
Public Structure Complex
	Implements IComparable, IFormattable

[SerializableAttribute]
public value class Complex : IComparable, 
	IFormattable

[<SealedAttribute>]
[<SerializableAttribute>]
type Complex =  
    struct
        interface IComparable
        interface IFormattable
    end

The Complex type exposes the following members.

Constructors

	Name	Description
	Complex(Double)	Constructs a Complex with a zero imaginary part.
	Complex(Complex)	Constructs a Complex equal to the argument.
	Complex(Double, Double)	Constructs a Complex with real and imaginary parts given by the input arguments.

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Methods

	Name	Description
	Abs	Returns the absolute value (modulus) of a Complex, .
	Acos	Returns the inverse cosine (arc cosine) of a Complex, with branch cuts outside the interval [-1,1] along the real axis.
	Acosh	Returns the inverse hyperbolic cosine (arc cosh) of a Complex, with a branch cut at values less than one along the real axis.
	Add(Double, Complex)	Returns the sum of a double and a Complex, x+y.
	Add(Complex, Complex)	Returns the sum of two Complex objects, x+y.
	Add(Complex, Double)	Returns the sum of a Complex and a double, x+y.
	Argument	Returns the argument (phase) of a Complex, in radians, with a branch cut along the negative real axis.
	Asin	Returns the inverse sine (arc sine) of a Complex, with branch cuts outside the interval [-1,1] along the real axis.
	Asinh	Returns the inverse hyperbolic sine (arc sinh) of a Complex, with branch cuts outside the interval [-i,i].
	Atan	Returns the inverse tangent (arc tangent) of a Complex, with branch cuts outside the interval [-i,i] along the imaginary axis.
	Atanh	Returns the inverse hyperbolic tangent (arc tanh) of a Complex, with branch cuts outside the interval [-1,1] on the real axis.
	CompareTo(Object)	Compares this Complex to another Object.
	CompareTo(Complex)	Compares two Complex objects.
	Conjugate	Returns the complex conjugate of a Complex object.
	Cos	Returns the cosine of a Complex.
	Cosh	Returns the hyperbolic cosh of a Complex.
	Divide(Double, Complex)	Returns the result of a double divided by a Complex object, x/y.
	Divide(Complex, Complex)	Returns the result of a Complex object divided by a Complex object, x/y.
	Divide(Complex, Double)	Returns the result of a Complex object divided by a double, x/y.
	Equals	Compares this object against the specified object. (Overrides ValueTypeEquals(Object).)
	Exp	Returns the exponential of a Complex z, exp(z).
	GetHashCode	Returns a hashcode for this Complex. (Overrides ValueTypeGetHashCode.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Imag	Returns the imaginary part of a Complex object.
	Imag(Complex)	Returns the imaginary part of a Complex object.
	Log	Returns the logarithm of a Complex z, with a branch cut along the negative real axis.
	Multiply(Double, Complex)	Returns the product of a double and a Complex object, x y*.
	Multiply(Complex, Complex)	Returns the product of two Complex objects, x y*.
	Multiply(Complex, Double)	Returns the product of a Complex object and a double, x y*.
	MultiplyImag(Double, Complex)	Returns the product of a pure imaginary double and a Complex object, ix y*.
	MultiplyImag(Complex, Double)	Returns the product of a Complex object and a pure imaginary double, x * iy.
	Negate	Returns the negative of a Complex object, -z.
	Parse(String)	Converts the string representation of a number in a specified style to its Complex number equivalent.
	Parse(String, IFormatProvider)	Converts the string representation of a number in a specified style to its Complex number equivalent.
	Pow(Complex, Complex)	Returns the Complex x raised to the Complex y power.
	Pow(Complex, Double)	Returns the Complex z raised to the x power, with a branch cut for the first parameter (z) along the negative real axis.
	Real	Returns the real part of a Complex object.
	Real(Complex)	Returns the real part of a Complex object.
	Sin	Returns the sine of a Complex.
	Sinh	Returns the hyperbolic sine of a Complex.
	Sqrt	Returns the square root of a Complex, with a branch cut along the negative real axis.
	Subtract(Double, Complex)	Returns the difference of a double and a Complex object, x-y.
	Subtract(Complex, Complex)	Returns the difference of two Complex objects, x-y.
	Subtract(Complex, Double)	Returns the difference of a Complex object and a double, x-y.
	Tan	Returns the tangent of a Complex.
	Tanh	Returns the hyperbolic tanh of a Complex.
	ToString	Returns a String representation for the specified Complex. (Overrides ValueTypeToString.)
	ToString(String, IFormatProvider)	Formats the value of the current instance using the specified format.

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Operators

	Name	Description
	Addition(Double, Complex)	Returns the sum of a double and a Complex, x+y.
	Addition(Complex, Complex)	Returns the sum of two Complex objects, x+y.
	Addition(Complex, Double)	Returns the sum of a Complex and a double, x+y.
	Division(Double, Complex)	Returns the result of a double divided by a Complex object, x/y.
	Division(Complex, Complex)	Returns the result of a Complex object divided by a Complex object, x/y.
	Division(Complex, Double)	Returns the result of a Complex object divided by a double, x/y.
	Equality(Double, Complex)	Returns true if x and y are equal.
	Equality(Complex, Complex)	Returns true if x and y are equal.
	Equality(Complex, Double)	Returns true if x and y are equal.
	Inequality(Double, Complex)	Returns true if x and y are not equal.
	Inequality(Complex, Complex)	Returns true if x and y are not equal.
	Inequality(Complex, Double)	Returns true if x and y are not equal.
	Multiply(Double, Complex)	Returns the product of a double and a Complex object, x y*.
	Multiply(Complex, Complex)	Returns the product of two Complex objects, x y*.
	Multiply(Complex, Double)	Returns the product of a Complex object and a double, x y*.
	Subtraction(Double, Complex)	Returns the difference of a double and a Complex object, x-y.
	Subtraction(Complex, Complex)	Returns the difference of two Complex objects, x-y.
	Subtraction(Complex, Double)	Returns the difference of a Complex object and a double, x-y.
	UnaryNegation	Returns the negative of a Complex object, -x.

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Fields

	Name	Description
	I	The imaginary unit.

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Remarks

The binary operations have the form, where op is Add, Subtract, Multiply or Divide.

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public static Complex op(Complex x, Complex y)   // x op y
public static Complex op(Complex x, double y)    // x op y
public static Complex op(double x, Complex y)    // x op y

Complex objects are immutable. Once created there is no way to change their value. The functions in this class follow the rules for complex arithmetic as defined C9x Annex G: IEC 559-compatible complex arithmetic. The API is not the same, but handling of infinities, NaNs, and positive and negative zeros is intended to follow the same rules.

Reference

Imsl.Math Namespace

Other Resources

Example