Struct Complex

Structure defining a complex number.

Implements

IEquatable<Complex>

IDotProduct<Complex, Complex>

INorm<Complex>

IMetric<Complex>

IGroupAction<Complex, Double>

IGroupAction<Complex, Real>

Namespace: BRIDGES.Arithmetic.Numbers

Assembly: BRIDGES.dll

Syntax

public struct Complex : IDotProduct<Complex, Complex>, INorm<Complex>, IMetric<Complex>, IGroupAction<Complex, double>, IGroupAction<Complex, Real>

Constructors

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Complex(Complex)

Initialises a new instance of Complex structure from another Complex numbers.

Declaration

public Complex(Complex complex)

Parameters

Type	Name	Description
Complex	complex	Complex number to deep copy.

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Complex(Double, Double)

Initialises a new instance of Complex structure by defining it real and imaginary parts.

Declaration

public Complex(double real, double imaginary)

Parameters

Type	Name	Description
Double	real	Value of the real part.
Double	imaginary	Value of the imaginary part.

Properties

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Argument

Gets the argument of this Complex number.

Declaration

public readonly double Argument { get; }

Property Value

Type	Description
Double

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ImaginaryOne

Gets a new instance of the Complex structure equal to the unit imaginary element : (0.0, 1.0).

Declaration

public static readonly Complex ImaginaryOne { get; }

Property Value

Type	Description
Complex	The new Complex number equal to imaginary one.

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ImaginaryPart

Gets or sets the imaginary component of this Complex number.

Declaration

public double ImaginaryPart { get; set; }

Property Value

Type	Description
Double

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Modulus

Gets the modulus of this Complex number.

Declaration

public readonly double Modulus { get; }

Property Value

Type	Description
Double

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One

Gets a new instance of the Complex structure equal to the multiplicative neutral element : (0.0, 1.0).

Declaration

public static readonly Complex One { get; }

Property Value

Type	Description
Complex	The new Complex number equal to one.

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RealPart

Gets or sets the real component of this Complex number.

Declaration

public double RealPart { get; set; }

Property Value

Type	Description
Double

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Zero

Gets a new instance of the Complex structure equal to the additive neutral element : (0.0, 1.0).

Declaration

public static readonly Complex Zero { get; }

Property Value

Type	Description
Complex	The new Complex number equal to zero.

Methods

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Add(Complex, Complex)

Computes the addition of two Complex numbers.

Declaration

public static Complex Add(Complex left, Complex right)

Parameters

Type	Name	Description
Complex	left	Complex number for the addition.
Complex	right	Complex number for the addition.

Returns

Type	Description
Complex	The new Complex number resulting from the addition.

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Add(Complex, Real)

Computes the right addition of a Complex number with a Real number.

Declaration

public static Complex Add(Complex left, Real right)

Parameters

Type	Name	Description
Complex	left	Complex number for the addition.
Real	right	Real number for the addition.

Returns

Type	Description
Complex	The new Complex number resulting from the addition.

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Add(Real, Complex)

Computes the left addition of a Complex number with a Real number.

Declaration

public static Complex Add(Real left, Complex right)

Parameters

Type	Name	Description
Real	left	Real number for the addition.
Complex	right	Complex number for the addition.

Returns

Type	Description
Complex	The new Complex number resulting from the addition.

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Conjugate(Complex)

Gets the conjugate value of a Complex number.

Declaration

public static Complex Conjugate(Complex complex)

Parameters

Type	Name	Description
Complex	complex	Complex number from which the conjugate is computed.

Returns

Type	Description
Complex	The new Complex number, conjugate of the initial one.

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DistanceTo(Complex)

Computes the distance of this element to another element.

Declaration

public double DistanceTo(Complex other)

Parameters

Type	Name	Description
Complex	other

Returns

Type	Description
Double	The value of the distance between the two elements.

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Divide(Complex, Complex)

Computes the division of two Complex numbers.

Declaration

public static Complex Divide(Complex left, Complex right)

Parameters

Type	Name	Description
Complex	left	Complex number to divide.
Complex	right	Complex number to divide with.

Returns

Type	Description
Complex	The new Complex number resulting from the division.

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Divide(Complex, Real)

Computes the division of a Complex number with a Real number.

Declaration

public static Complex Divide(Complex left, Real right)

Parameters

Type	Name	Description
Complex	left	Complex number to divide.
Real	right	Real number to divide with.

Returns

Type	Description
Complex	The new Complex number resulting from the division.

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Divide(Complex, Double)

Computes the scalar division of a Complex number with a number.

Declaration

public static Complex Divide(Complex operand, double divisor)

Parameters

Type	Name	Description
Complex	operand	Complex number to divide.
Double	divisor	number to divide with.

Returns

Type	Description
Complex	The new Complex number resulting from the scalar division.

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Divide(Real, Complex)

Computes the division of a Real number with a Complex number.

Declaration

public static Complex Divide(Real left, Complex right)

Parameters

Type	Name	Description
Real	left	Real number to divide.
Complex	right	Complex number to divide with.

Returns

Type	Description
Complex	The new Complex number resulting from the division.

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DotProduct(Complex)

Computes the hermitian dot product of this Complex number with another Complex number.

Declaration

public Complex DotProduct(Complex other)

Parameters

Type	Name	Description
Complex	other	Right Complex for number the dot product.

Returns

Type	Description
Complex	The value of the dot product of the two elements.

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Equals(Complex)

Structure defining a complex number.

Declaration

public bool Equals(Complex other)

Parameters

Type	Name	Description
Complex	other

Returns

Type	Description
Boolean

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Equals(Object)

Structure defining a complex number.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
Object	obj

Returns

Type	Description
Boolean

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FromPolarCoordinates(Double, Double)

Gets a new Complex number by defining its polar coordinates.

Declaration

public static Complex FromPolarCoordinates(double modulus, double argument)

Parameters

Type	Name	Description
Double	modulus	Value of the modulus.
Double	argument	Value of the argument (in radians).

Returns

Type	Description
Complex	The new Complex number.

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GetHashCode()

Structure defining a complex number.

Declaration

public override int GetHashCode()

Returns

Type	Description
Int32

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Inverse(Complex)

Computes the inverse of the given Complex number.

Declaration

public static Complex Inverse(Complex operand)

Parameters

Type	Name	Description
Complex	operand	Complex from which the inverse is computed.

Returns

Type	Description
Complex	The new Complex number, inverse of the initial one.

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Multiply(Complex, Complex)

Computes the multiplication of two Complex numbers.

Declaration

public static Complex Multiply(Complex left, Complex right)

Parameters

Type	Name	Description
Complex	left	Complex number for the multiplication.
Complex	right	Complex number for the multiplication.

Returns

Type	Description
Complex	The new Complex number resulting from the multiplication.

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Multiply(Complex, Real)

Computes the right multiplication of a Complex number with a Real number.

Declaration

public static Complex Multiply(Complex left, Real right)

Parameters

Type	Name	Description
Complex	left	Complex number for the multiplicaion.
Real	right	Real number for the multiplicaion.

Returns

Type	Description
Complex	The new Complex number resulting from the multiplication.

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Multiply(Complex, Double)

Computes the right scalar multiplication of a Complex number with a number.

Declaration

public static Complex Multiply(Complex operand, double factor)

Parameters

Type	Name	Description
Complex	operand	Complex number to multiply.
Double	factor	number.

Returns

Type	Description
Complex	The new Complex number resulting from the right scalar multiplication.

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Multiply(Real, Complex)

Computes the left multiplication of a Complex number with a Real number.

Declaration

public static Complex Multiply(Real left, Complex right)

Parameters

Type	Name	Description
Real	left	Real number for the multiplicaion.
Complex	right	Complex number for the multiplicaion.

Returns

Type	Description
Complex	The new Complex number resulting from the multiplication.

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Multiply(Double, Complex)

Computes the left scalar multiplication of a Complex number with a number.

Declaration

public static Complex Multiply(double factor, Complex operand)

Parameters

Type	Name	Description
Double	factor	number.
Complex	operand	Complex number to multiply.

Returns

Type	Description
Complex	The new Complex number resulting from the left scalar multiplication.

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Norm()

Computes the norm of this element.

Declaration

public double Norm()

Returns

Type	Description
Double	The value of the norm.

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Opposite(Complex)

Computes the opposite of the given Complex number.

Declaration

public static Complex Opposite(Complex operand)

Parameters

Type	Name	Description
Complex	operand	Complex number from which the opposite is computed.

Returns

Type	Description
Complex	The new Complex number, opposite of the initial one.

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Subtract(Complex, Complex)

Computes the subtraction of two Complex numbers.

Declaration

public static Complex Subtract(Complex left, Complex right)

Parameters

Type	Name	Description
Complex	left	Complex number to subtract.
Complex	right	Complex number to subtract with.

Returns

Type	Description
Complex	The new Complex number resulting from the subtraction.

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Subtract(Complex, Real)

Computes the subtraction of a Complex number with a Real number.

Declaration

public static Complex Subtract(Complex left, Real right)

Parameters

Type	Name	Description
Complex	left	Complex number to subtract.
Real	right	Real number to subtract with.

Returns

Type	Description
Complex	The new Complex number resulting from the subtraction.

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Subtract(Real, Complex)

Computes the subtraction of a Real number with a Complex number.

Declaration

public static Complex Subtract(Real left, Complex right)

Parameters

Type	Name	Description
Real	left	Real number to subtract.
Complex	right	Complex number to subtract with.

Returns

Type	Description
Complex	The new Complex number resulting from the subtraction.

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ToString()

Structure defining a complex number.

Declaration

public override string ToString()

Returns

Type	Description
String

Operators

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Addition(Complex, Complex)

Computes the addition of two Complex numbers.

Declaration

public static Complex operator +(Complex left, Complex right)

Parameters

Type	Name	Description
Complex	left	Complex number for the addition.
Complex	right	Complex number for the addition.

Returns

Type	Description
Complex	The new Complex number resulting from the addition.

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Addition(Complex, Real)

Computes the right addition of a Complex number with a Real number.

Declaration

public static Complex operator +(Complex left, Real right)

Parameters

Type	Name	Description
Complex	left	Complex number for the addition.
Real	right	Real number for the addition.

Returns

Type	Description
Complex	The new Complex number resulting from the addition.

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Addition(Complex, Double)

Computes the right addition of a Complex number with a number.

Declaration

public static Complex operator +(Complex left, double right)

Parameters

Type	Name	Description
Complex	left	Complex number for the addition.
Double	right	number for the addition.

Returns

Type	Description
Complex	The new Complex number resulting from the addition.

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Addition(Real, Complex)

Computes the left addition of a Complex number with a Real number.

Declaration

public static Complex operator +(Real left, Complex right)

Parameters

Type	Name	Description
Real	left	Real number for the addition.
Complex	right	Complex number for the addition.

Returns

Type	Description
Complex	The new Complex number resulting from the addition.

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Addition(Double, Complex)

Computes the left addition of a Complex number with a number.

Declaration

public static Complex operator +(double left, Complex right)

Parameters

Type	Name	Description
Double	left	number for the addition.
Complex	right	Complex number for the addition.

Returns

Type	Description
Complex	The new Complex number resulting from the addition.

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Division(Complex, Complex)

Computes the division of two Complex numbers.

Declaration

public static Complex operator /(Complex left, Complex right)

Parameters

Type	Name	Description
Complex	left	Complex number to divide.
Complex	right	Complex number to divide with.

Returns

Type	Description
Complex	The new Complex number resulting from the division.

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Division(Complex, Real)

Computes the division of a Complex number with a Real number.

Declaration

public static Complex operator /(Complex left, Real right)

Parameters

Type	Name	Description
Complex	left	Complex number to divide.
Real	right	Real number to divide with.

Returns

Type	Description
Complex	The new Complex number resulting from the division.

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Division(Complex, Double)

Computes the division of a Complex number with a number.

Declaration

public static Complex operator /(Complex left, double right)

Parameters

Type	Name	Description
Complex	left	Complex number to divide.
Double	right	number to divide with.

Returns

Type	Description
Complex	The new Complex number resulting from the division.

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Division(Real, Complex)

Computes the division of a Real number with a Complex number.

Declaration

public static Complex operator /(Real left, Complex right)

Parameters

Type	Name	Description
Real	left	Real number to divide.
Complex	right	Complex number to divide with.

Returns

Type	Description
Complex	The new Complex number resulting from the division.

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Division(Double, Complex)

Computes the division of a number with a Complex number.

Declaration

public static Complex operator /(double left, Complex right)

Parameters

Type	Name	Description
Double	left	number to divide.
Complex	right	Complex number to divide with.

Returns

Type	Description
Complex	The new Complex number resulting from the division.

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Explicit(Real to Complex)

Converts a Real number into a Complex number.

Declaration

public static explicit operator Complex(Real real)

Parameters

Type	Name	Description
Real	real	Real number to convert.

Returns

Type	Description
Complex	The new Complex number resulting from the conversion.

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Explicit(Double to Complex)

Converts a -precision real number into a Complex number.

Declaration

public static explicit operator Complex(double number)

Parameters

Type	Name	Description
Double	number	-precision real number to convert.

Returns

Type	Description
Complex	The new Complex number resulting from the conversion.

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Explicit(ValueTuple<Double, Double> to Complex)

Converts a into a Complex number.

Declaration

public static explicit operator Complex(ValueTuple<double, double> pair)

Parameters

Type	Name	Description
ValueTuple<Double, Double>	pair	to convert.

Returns

Type	Description
Complex	The new Complex number resulting from the conversion.

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Multiply(Complex, Complex)

Computes the multiplication of two Complex numbers.

Declaration

public static Complex operator *(Complex left, Complex right)

Parameters

Type	Name	Description
Complex	left	Complex number for the multiplication.
Complex	right	Complex number for the multiplication.

Returns

Type	Description
Complex	The new Complex number resulting from the multiplication.

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Multiply(Complex, Real)

Computes the right multiplication of a Complex number with a Real number.

Declaration

public static Complex operator *(Complex left, Real right)

Parameters

Type	Name	Description
Complex	left	Complex number for the multiplicaion.
Real	right	Real number for the multiplicaion.

Returns

Type	Description
Complex	The new Complex number resulting from the multiplication.

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Multiply(Complex, Double)

Computes the right multiplication of a Complex number with a -precision real number.

Declaration

public static Complex operator *(Complex left, double right)

Parameters

Type	Name	Description
Complex	left	Complex number for the multiplicaion.
Double	right	number for the multiplicaion.

Returns

Type	Description
Complex	The new Complex number resulting from the multiplication.

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Multiply(Real, Complex)

Computes the left multiplication of a Complex number with a Real number.

Declaration

public static Complex operator *(Real left, Complex right)

Parameters

Type	Name	Description
Real	left	Real number for the multiplicaion.
Complex	right	Complex number for the multiplicaion.

Returns

Type	Description
Complex	The new Complex number resulting from the multiplication.

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Multiply(Double, Complex)

Computes the left multiplication of a number with a Complex number.

Declaration

public static Complex operator *(double left, Complex right)

Parameters

Type	Name	Description
Double	left	number for the multiplicaion.
Complex	right	Complex number for the multiplicaion.

Returns

Type	Description
Complex	The new Complex number resulting from the multiplication.

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Subtraction(Complex, Complex)

Computes the subtraction of two Complex numbers.

Declaration

public static Complex operator -(Complex left, Complex right)

Parameters

Type	Name	Description
Complex	left	Complex number to subtract.
Complex	right	Complex number to subtract with.

Returns

Type	Description
Complex	The new Complex number resulting from the subtraction.

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Subtraction(Complex, Real)

Computes the subtraction of a Complex number with a Real number.

Declaration

public static Complex operator -(Complex left, Real right)

Parameters

Type	Name	Description
Complex	left	Complex number to subtract.
Real	right	Real number to subtract with.

Returns

Type	Description
Complex	The new Complex number resulting from the subtraction.

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Subtraction(Complex, Double)

Computes the subtraction of a Complex number with a number.

Declaration

public static Complex operator -(Complex left, double right)

Parameters

Type	Name	Description
Complex	left	Complex number to subtract.
Double	right	number to subtract with.

Returns

Type	Description
Complex	The new Complex number resulting from the subtraction.

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Subtraction(Real, Complex)

Computes the subtraction of a Real number with a Complex number.

Declaration

public static Complex operator -(Real left, Complex right)

Parameters

Type	Name	Description
Real	left	Real number to subtract.
Complex	right	Complex number to subtract with.

Returns

Type	Description
Complex	The new Complex number resulting from the subtraction.

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Subtraction(Double, Complex)

Computes the subtraction of a number with a Complex number.

Declaration

public static Complex operator -(double left, Complex right)

Parameters

Type	Name	Description
Double	left	number to subtract.
Complex	right	Complex number to subtract with.

Returns

Type	Description
Complex	The new Complex number resulting from the subtraction.

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UnaryNegation(Complex)

Computes the opposite of the given Complex number.

Declaration

public static Complex operator -(Complex operand)

Parameters

Type	Name	Description
Complex	operand	Complex number from which the opposite is computed.

Returns

Type	Description
Complex	The new Complex number, opposite of the initial one.

Explicit Interface Implementations

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IGroupAction<Complex, Real>.Divide(Real)

Computes the right scalar division of the current element.

Declaration

Complex IGroupAction<Complex, Real>.Divide(Real divisor)

Parameters

Type	Name	Description
Real	divisor

Returns

Type	Description
Complex	The new element resulting from the scalar dividion.

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IGroupAction<Complex, Real>.Multiply(Real)

Computes the right scalar multiplication of the current element.

Declaration

Complex IGroupAction<Complex, Real>.Multiply(Real factor)

Parameters

Type	Name	Description
Real	factor

Returns

Type	Description
Complex	The new element resulting from the scalar multiplication.

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IGroupAction<Complex, Double>.Divide(Double)

Computes the right scalar division of the current element.

Declaration

Complex IGroupAction<Complex, double>.Divide(double divisor)

Parameters

Type	Name	Description
Double	divisor

Returns

Type	Description
Complex	The new element resulting from the scalar dividion.

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IGroupAction<Complex, Double>.Multiply(Double)

Computes the right scalar multiplication of the current element.

Declaration

Complex IGroupAction<Complex, double>.Multiply(double factor)

Parameters

Type	Name	Description
Double	factor

Returns

Type	Description
Complex	The new element resulting from the scalar multiplication.

Implements

IEquatable<>

IDotProduct<TSelf, TValue>

INorm<TSelf>

IMetric<TSelf>

IGroupAction<TSelf, TValue>