[SerializableAttribute]
public struct DoubleComplex : IEquatable<DoubleComplex>, 
	IEquatable<double>, IStructuralEquatable

<SerializableAttribute>
Public Structure DoubleComplex
	Implements IEquatable(Of DoubleComplex), IEquatable(Of Double), 
	IStructuralEquatable

[SerializableAttribute]
public value class DoubleComplex : IEquatable<DoubleComplex>, 
	IEquatable<double>, IStructuralEquatable

[<SealedAttribute>]
[<SerializableAttribute>]
type DoubleComplex =  
    struct
        interface IEquatable<DoubleComplex>
        interface IEquatable<float>
        interface IStructuralEquatable
    end

The DoubleComplex type exposes the following members.

	Name	Description
	DoubleComplex(Double)	Constructs a complex number from a real number.
	DoubleComplex(Double, Double)	Constructs a complex number from its real and imaginary parts.
	DoubleComplex(Double, Double, Boolean)	Obsolete. Constructs a complex number from rectangular or polar components.

	Name	Description
	Argument	Obsolete. Gets the argument of a DoubleComplex number.
	Im	Gets the imaginary part of the complex number.
	IsImaginary	Indicates whether a DoubleComplex number is a pure imaginary number.
	IsReal	Indicates whether a DoubleComplex number is, in fact, real.
	IsZero	Indicates whether a DoubleComplex number is equal to zero.
	Magnitude	Gets the magnitude (modulus or absolute value) of a DoubleComplex number.
	MagnitudeSquared	Returns the square of the modulus of a DoubleComplex number.
	Modulus	Obsolete. Gets the magnitude (modulus or absolute value) of a DoubleComplex number.
	ModulusSquared	Obsolete. Returns the square of the modulus of a DoubleComplex number.
	OneNorm	Gets the sum of the absolute values of the real and imaginary parts of the complex number.
	Phase	Gets the phase or argument of a DoubleComplex number.
	Re	Gets the real part of the DoubleComplex number.

	Name	Description
	Abs	Returns the absolute value of a DoubleComplex number.
	Acos(Double)	Gets the inverse cosine of a real number.
	Acos(DoubleComplex)	Gets the inverse cosine of a DoubleComplex number.
	Acosh	Gets the inverse hyperbolic cosine of a DoubleComplex number.
	Add(Double, DoubleComplex)	Adds a DoubleComplex number to a real number.
	Add(DoubleComplex, DoubleComplex)	Adds two DoubleComplex numbers.
	Add(DoubleComplex, Double)	Adds a DoubleComplex number to a real number.
	Arg	Returns the argument of a DoubleComplex number.
	Asin(Double)	Gets the inverse sine of a real number.
	Asin(DoubleComplex)	Gets the inverse sine of a DoubleComplex number.
	Asinh	Gets the inverse hyperbolic sine of a DoubleComplex number.
	Atan	Gets the inverse tangent of a DoubleComplex number.
	Atanh	Gets the inverse hyperbolic tangent of a DoubleComplex number.
	Conjugate	Returns the conjugate of this complex number.
	Conjugate(DoubleComplex)	Returns the conjugate of a DoubleComplex number.
	ConjugateMultiply	Multiplies the Conjugate(DoubleComplex) of a DoubleComplex number and a second DoubleComplex number.
	Cos	Gets the cosine of a DoubleComplex number.
	Cosh	Gets the hyperbolic cosine of a DoubleComplex number.
	Decrement	Decrements the real part of a DoubleComplex number by one.
	Divide(Double, DoubleComplex)	Divides a real number by a DoubleComplex number.
	Divide(DoubleComplex, DoubleComplex)	Divides a DoubleComplex number by another.
	Divide(DoubleComplex, Double)	Divides a DoubleComplex number by a real number.
	Equals(Double)	Compares a complex number to a real number.
	Equals(Object)	Overridden. Returns a value indicating whether this instance is equal to a specified object. (Overrides ValueTypeEquals(Object).)
	Equals(DoubleComplex)	Compares a complex number to another complex number.
	Equals(Object, IEqualityComparer)	Overridden. Returns a value indicating whether this instance is equal to a specified object.
	Exp	Returns e raised to the specified power.
	ExpI	Evaluates the exponential function for an imaginary argument.
	ExpMinus1	Returns the exponential function minus 1.
	FromPolar	Constructs a complex number from polar components.
	GetHashCode	Overridden. Returns the hash code for this instance. (Overrides ValueTypeGetHashCode.)
	GetHashCode(IEqualityComparer)	Overridden. Returns the hash code for this instance.
	GetImaginaryPart	Returns an array of Doubles that contains the imaginary parts of an array of DoubleComplex numbers.
	GetRealPart	Returns an array of Doubles that contains the real parts of an array of DoubleComplex numbers.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Imaginary	Constructs a complex number that has a purely imaginary value.
	Increment	Increments the real part of a DoubleComplex number by one.
	IsInfinity	Indicates whether a DoubleComplex number is infinite.
	IsNaN	Indicates whether a DoubleComplex number is undefined.
	Log(DoubleComplex)	Returns the natural logarithm of a DoubleComplex number.
	Log(DoubleComplex, DoubleComplex)	Returns the logarithm of a DoubleComplex number to the specified base.
	Log10	Returns the base 10 logarithm of a DoubleComplex number.
	Log1PlusX	Returns the logarithm of 1 plus the argument.
	Multiply(Double, DoubleComplex)	Multiplies a DoubleComplex number and a real number.
	Multiply(DoubleComplex, DoubleComplex)	Multiplies two DoubleComplex numbers.
	Multiply(DoubleComplex, Double)	Multiplies a DoubleComplex number and a real number.
	Negate	Negates a DoubleComplex number.
	Plus	Applies the unary plus operator to a DoubleComplex number.
	Pow(DoubleComplex, DoubleComplex)	Returns a DoubleComplex number raised to the specified power.
	Pow(DoubleComplex, Double)	Returns a DoubleComplex number raised to the specified power.
	Pow(DoubleComplex, Int32)	Returns a DoubleComplex number raised to the specified integer power.
	RootOfUnity	Returns a complex number that is the specified root of unity of the specified degree.
	Sin	Gets the sine of a DoubleComplex number.
	Sinh	Gets the hyperbolic sine of a DoubleComplex number.
	Sqrt(Double)	Returns the first square root of a real number.
	Sqrt(DoubleComplex)	Returns the first square root of a DoubleComplex number.
	Subtract(Double, DoubleComplex)	Subtracts a DoubleComplex number from a real number.
	Subtract(DoubleComplex, DoubleComplex)	Subtracts two DoubleComplex numbers.
	Subtract(DoubleComplex, Double)	Subtracts a real number from a DoubleComplex number.
	Tan	Gets the tangent of a DoubleComplex number.
	Tanh	Gets the hyperbolic tangent of a DoubleComplex number.
	ToString	Converts the numeric value of this instance to its equivalent string representation. (Overrides ValueTypeToString.)
	ToString(IFormatProvider)	Converts the numeric value of this instance to its equivalent string representation using the specified culture-specific format information.
	ToString(String)	Converts the numeric value of this instance to its equivalent string representation using the specified format.
	ToString(String, IFormatProvider)	Converts the numeric value of this instance to its equivalent string representation using the specified format and culture-specific format information.

	Name	Description
	Addition(Double, DoubleComplex)	Adds a DoubleComplex number to a real number.
	Addition(DoubleComplex, DoubleComplex)	Adds two DoubleComplex numbers.
	Addition(DoubleComplex, Double)	Adds a DoubleComplex number to a real number.
	Decrement	Decrements the real part of a DoubleComplex number by one.
	Division(Double, DoubleComplex)	Divides a real number by a DoubleComplex number.
	Division(DoubleComplex, DoubleComplex)	Divides a DoubleComplex number by another.
	Division(DoubleComplex, Double)	Divides a DoubleComplex number by a real number.
	Equality(Double, DoubleComplex)	Compares a DoubleComplex number and a real number for equality.
	Equality(DoubleComplex, DoubleComplex)	Compares two DoubleComplex numbers for equality.
	Equality(DoubleComplex, Double)	Compares a DoubleComplex number and a real number for equality.
	(DoubleComplex to Double)	Casts a DoubleComplex number to a real number. The imaginary part must be zero.
	(Double to DoubleComplex)	Casts a real number to a DoubleComplex type.
	Increment	Increments the real part of a DoubleComplex number by one.
	Inequality(Double, DoubleComplex)	Compares a DoubleComplex number and a real number for inequality.
	Inequality(DoubleComplex, DoubleComplex)	Compares two DoubleComplex numbers for inequality.
	Inequality(DoubleComplex, Double)	Compares a DoubleComplex number and a real number for inequality.
	Multiply(Double, DoubleComplex)	Multiplies a DoubleComplex number and a real number.
	Multiply(DoubleComplex, DoubleComplex)	Multiplies two DoubleComplex numbers.
	Multiply(DoubleComplex, Double)	Multiplies a DoubleComplex number and a real number.
	Subtraction(Double, DoubleComplex)	Subtracts a DoubleComplex number from a real number.
	Subtraction(DoubleComplex, DoubleComplex)	Subtracts two DoubleComplex numbers.
	Subtraction(DoubleComplex, Double)	Subtracts a real number from a DoubleComplex number.
	UnaryNegation	Negates a DoubleComplex number.
	UnaryPlus	Applies the unary plus operator to a DoubleComplex number.

	Name	Description
	I	Represents the square root of -1.
	Infinity	Represents complex infinity.
	NaN	Represents complex NaN, or Not a Number.
	One	Represents the complex number one.
	Zero	Represents the complex number zero.

The DoubleComplex value type represents a complex number made of double-precision, 64-bit real and imaginary parts.

DoubleComplex numbers arise in algebra in the solution of quadratic equations. The equation x²= –1 does not have any real solutions. However, if we define a new number, i as the square root of -1, then we have two solutions: i and -i.

This, in turn, gives rise to an entirely new class of numbers of the form a + ib with a and b real, and i defined as above. These are the complex numbers.

The DoubleComplex structure provides methods for all the common operations on complex numbers. The Re property returns the real component of the complex number, while Im returns the imaginary part. Because the complex numbers don't have a natural ordering, only equality and inequality operators are available.

Overloaded versions of the major arithmetic operators are provided for languages that support them. For languages that don't support operator overloading, equivalent methods are supplied.

When performing binary operations, if one of the operands is a DoubleComplex, then the other operand is required to be an integral type or a floating-point type (Double or Single) or a complex type (DoubleComplex). Prior to performing the operation, if the other operand is not a DoubleComplex, it is converted to DoubleComplex, and the operation is performed using at least double precision. If the operation produces a numeric result, the type of the result is DoubleComplex.

Exceptions to this are methods that return a real property of a complex number: Phase, Magnitude, MagnitudeSquared and Abs(DoubleComplex). These methods return a Double value.

The floating-point operators, including the assignment operators, do not throw exceptions. Instead, in exceptional situations, the result of a floating-point operation is zero, Infinity, or NaN, as described below:

• If the result of a complex floating-point operation is too small for the destination format, the result of the operation is zero.
• If the magnitude of the complex result of a floating-point operation is too large for the destination format, the result of the operation is Infinity. Directed infinities are currently not supported.
• If a complex floating-point operation is invalid, the result of the operation is NaN.
• If one or both operands of a complex floating-point operation are NaN, the result of the operation is NaN.

Many elementary functions have been extended to the complex domain. These are implemented by static methods.

Some of these functions are multi-valued. If there is one real argument, then any symmetry or anti-symmetry about the origin is preserved. For example, the inverse sine function satisfies asin(-x) == -asin(x) for -1 <= x <= 1. The Asin(Double) method satisfies this relationship for any real value of x.

For complex arguments, the identity Conjugate(f(x)) == f(Conjugate(x)) is preserved. The branch cuts for all complex functions defined here are along either the real or the imaginary axis. Along the branch cuts, the functions have different values depending on whether the zero component is normal (positive) zero or negative zero.

The real and imaginary parts of DoubleComplex numbers are double-precision floating-point numbers.

Numerical Libraries

Reference