Complex.Multiply Method

Definition

Namespace:

System.Numerics

Assembly:

System.Runtime.Numerics.dll

Multiplies a specified number by another specified number, where at least one of them is a complex number, and the other could be a double-precision real number.

Overloads

Multiply(Double, Complex)	Returns the product of a double-precision real number and a complex number.
Multiply(Complex, Double)	Returns the product of a complex number and a double-precision real number.
Multiply(Complex, Complex)	Returns the product of two complex numbers.

Examples

The following example multiples a complex number by each element in an array of complex numbers.

using System;
using System.Numerics;

public class Example
{
   public static void Main()
   {
      Complex number1 = new Complex(8.3, 17.5);
      Complex[] numbers = { new Complex(1.4, 6.3),
                            new Complex(-2.7, 1.8),
                            new Complex(3.1, -2.1) };
      foreach (Complex number2 in numbers)
         Console.WriteLine("{0} x {1} = {2}", number1, number2,
                           Complex.Multiply(number1, number2));
   }
}
// The example displays the following output:
//       (8.3, 17.5) x (1.4, 6.3) = (-98.63, 76.79)
//       (8.3, 17.5) x (-2.7, 1.8) = (-53.91, -32.31)
//       (8.3, 17.5) x (3.1, -2.1) = (62.48, 36.82)

open System.Numerics

let number1 = Complex(8.3, 17.5)
let numbers = [ Complex(1.4, 6.3); Complex(-2.7, 1.8); Complex(3.1, -2.1) ]

for number2 in numbers do
    printfn $"{number1} x {number2} = {Complex.Multiply(number1, number2)}"
// The example displays the following output:
//       (8.3, 17.5) x (1.4, 6.3) = (-98.63, 76.79)
//       (8.3, 17.5) x (-2.7, 1.8) = (-53.91, -32.31)
//       (8.3, 17.5) x (3.1, -2.1) = (62.48, 36.82)

Imports System.Numerics

Module Example
   Public Sub Main()
      Dim number1 As New Complex(8.3, 17.5)
      Dim numbers() As Complex = { New Complex(1.4, 6.3), 
                                   New Complex(-2.7, 1.8), 
                                   New Complex(3.1, -2.1) }
      For Each number2 In numbers
         Console.WriteLine("{0} x {1} = {2}", number1, number2, 
                           Complex.Multiply(number1, number2))
      Next
   End Sub
End Module
' The example displays the following output:
'       (8.3, 17.5) x (1.4, 6.3) = (-98.63, 76.79)
'       (8.3, 17.5) x (-2.7, 1.8) = (-53.91, -32.31)
'       (8.3, 17.5) x (3.1, -2.1) = (62.48, 36.82)

Remarks

The Multiply methods allow performing multiplication operations that involve complex numbers.

If the multiplication results in an overflow in either the real or imaginary component, the value of that component is either Double.PositiveInfinity or Double.NegativeInfinity.

The Multiply method is implemented for Languages that don't support custom operators. Its behavior is identical to multiplication using the multiplication operator.

Multiply(Double, Complex)

Source:

Complex.cs

Returns the product of a double-precision real number and a complex number.

public:
 static System::Numerics::Complex Multiply(double left, System::Numerics::Complex right);

public static System.Numerics.Complex Multiply (double left, System.Numerics.Complex right);

static member Multiply : double * System.Numerics.Complex -> System.Numerics.Complex

Public Shared Function Multiply (left As Double, right As Complex) As Complex

Parameters

left

Double

The double-precision real number to multiply.

right

Complex

The complex number to multiply.

Returns

Complex

The product of the left and right parameters.

Remarks

The multiplication of a real number (which can be regarded as the complex number a + 0i) and a complex number (c + di) takes the following form:

$ac + adi$

See also

• Multiply(Double, Complex)

Multiply(Complex, Double)

Source:

Complex.cs

Returns the product of a complex number and a double-precision real number.

public:
 static System::Numerics::Complex Multiply(System::Numerics::Complex left, double right);

public static System.Numerics.Complex Multiply (System.Numerics.Complex left, double right);

static member Multiply : System.Numerics.Complex * double -> System.Numerics.Complex

Public Shared Function Multiply (left As Complex, right As Double) As Complex

Parameters

left

Complex

The complex number to multiply.

right

Double

The double-precision real number to multiply.

Returns

Complex

The product of the left and right parameters.

Remarks

The multiplication of a complex number (a + bi) and a real number (which can be regarded as the complex number c + 0i) takes the following form:

$ac + bci$

See also

• Multiply(Complex, Double)

Multiply(Complex, Complex)

Source:

Complex.cs

Returns the product of two complex numbers.

public:
 static System::Numerics::Complex Multiply(System::Numerics::Complex left, System::Numerics::Complex right);

public static System.Numerics.Complex Multiply (System.Numerics.Complex left, System.Numerics.Complex right);

static member Multiply : System.Numerics.Complex * System.Numerics.Complex -> System.Numerics.Complex

Public Shared Function Multiply (left As Complex, right As Complex) As Complex

Parameters

left

Complex

The first complex number to multiply.

right

Complex

The second complex number to multiply.

Returns

Complex

The product of the left and right parameters.

Remarks

The multiplication of a complex number, a + bi, and a second complex number, c + di, takes the following form:

$(ac - bd) + (ad + bc)i$

See also

• Multiply(Complex, Complex)