Complex.Reciprocal(Complex) Method
Definition
Important
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Returns the multiplicative inverse of a complex number.
public:
static System::Numerics::Complex Reciprocal(System::Numerics::Complex value);
public static System.Numerics.Complex Reciprocal (System.Numerics.Complex value);
static member Reciprocal : System.Numerics.Complex -> System.Numerics.Complex
Public Shared Function Reciprocal (value As Complex) As Complex
Parameters
- value
- Complex
A complex number.
Returns
The reciprocal of value
.
Examples
The following example uses the Reciprocal method to calculate the reciprocal values of several complex numbers. It also demonstrates that the result of multiplying a complex number by its reciprocal is Complex.One.
using System;
using System.Numerics;
public class Example
{
public static void Main()
{
Complex[] values = { new Complex(1, 1),
new Complex(-1, 1),
new Complex(10, -1),
new Complex(3, 5) };
foreach (Complex value in values)
{
Complex r1 = Complex.Reciprocal(value);
Console.WriteLine("{0:N0} x {1:N2} = {2:N2}",
value, r1, value * r1);
}
}
}
// The example displays the following output:
// (1, 1) x (0.50, -0.50) = (1.00, 0.00)
// (-1, 1) x (-0.50, -0.50) = (1.00, 0.00)
// (10, -1) x (0.10, 0.01) = (1.00, 0.00)
// (3, 5) x (0.09, -0.15) = (1.00, 0.00)
open System.Numerics
let values =
[ Complex(1., 1.); Complex(-1., 1.); Complex(10., -1.); Complex(3., 5.) ]
for value in values do
let r1 = Complex.Reciprocal value
printfn $"{value:N0} x {r1:N2} = {value * r1:N2}"
// The example displays the following output:
// (1, 1) x (0.50, -0.50) = (1.00, 0.00)
// (-1, 1) x (-0.50, -0.50) = (1.00, 0.00)
// (10, -1) x (0.10, 0.01) = (1.00, 0.00)
// (3, 5) x (0.09, -0.15) = (1.00, 0.00)
Imports System.Numerics
Module Example
Public Sub Main()
Dim values() As Complex = { New Complex(1, 1),
New Complex(-1, 1),
New Complex(10, -1),
New Complex(3, 5) }
For Each value As Complex In values
Dim r1 As Complex = Complex.Reciprocal(value)
Console.WriteLine("{0:N0} x {1:N2} = {2:N2}",
value, r1, value * r1)
Next
End Sub
End Module
' The example displays the following output:
' (1, 1) x (0.50, -0.50) = (1.00, 0.00)
' (-1, 1) x (-0.50, -0.50) = (1.00, 0.00)
' (10, -1) x (0.10, 0.01) = (1.00, 0.00)
' (3, 5) x (0.09, -0.15) = (1.00, 0.00)
Remarks
The reciprocal, or multiplicative inverse, of a number x is a number y where x multiplied by y yields 1. The reciprocal of a complex number is the complex number that produces Complex.One when the two numbers are multiplied. If a complex number is represented by a +bi, its reciprocal is represented by the expression a/(a2+b2) + -b/(a2 + b2).
If value is Complex.Zero, the method returns Complex.Zero. Otherwise, it returns the result of the expression Complex.One/value
.
Applies to
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