Numerical Components for .NET
Namespace: Extreme.MathematicsAssembly: Extreme.Numerics.SinglePrecision.Net40 (in Extreme.Numerics.SinglePrecision.Net40.dll) Version: 4.0.10170.0 (4.0.11003.0)
public struct SingleComplex : IEquatable<SingleComplex>,
Public Structure SingleComplex _
Implements IEquatable(Of SingleComplex), IEquatable(Of Single)
public value class SingleComplex : IEquatable<SingleComplex>,
type SingleComplex =
SingleComplex 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 SingleComplex 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
staticSharedstaticstatic (Shared in Visual Basic) methods are supplied.
When performing binary operations, if one of the
operands is a SingleComplex, then the other operand is
required to be an integral type or a floating-point type
(Single or Single) or a complex
Prior to performing the operation, if the other operand is
not a SingleComplex, it is converted to SingleComplex,
and the operation is performed using at least float precision.
If the operation produces a numeric
result, the type of the result is SingleComplex.
Exceptions to this are methods that return a real
property of a complex number: Argument,
Modulus, ModulusSquared and
Abs(SingleComplex). These methods return a Single
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:
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(Single)
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
The real and imaginary parts of SingleComplex
numbers are float-precision floating-point numbers.
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