Complex.Addition Operator

Definition

Namespace:

System.Numerics

Assembly:

System.Runtime.Numerics.dll

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

Overloads

Addition(Complex, Complex)	Adds two complex numbers.
Addition(Complex, Double)	Adds a complex number to a double-precision real number.
Addition(Double, Complex)	Adds a double-precision real number to a complex number.

Examples

The following example illustrates addition with complex numbers:

using System;
using System.Numerics;

public class Example
{
   public static void Main()
   {
      Complex[] values= { new Complex(12.3, -1.4),
                          new Complex(-6.2, 3.1),
                          new Complex(8.9, 1.5) };
      foreach (var c1 in values)
         foreach (var c2 in values)
            Console.WriteLine("{0} + {1} = {2}", c1, c2, c1 + c2);
   }
}
// The example displays the following output:
//       (12.3, -1.4) + (12.3, -1.4) = (24.6, -2.8)
//       (12.3, -1.4) + (-6.2, 3.1) = (6.1, 1.7)
//       (12.3, -1.4) + (8.9, 1.5) = (21.2, 0.1)
//       (-6.2, 3.1) + (12.3, -1.4) = (6.1, 1.7)
//       (-6.2, 3.1) + (-6.2, 3.1) = (-12.4, 6.2)
//       (-6.2, 3.1) + (8.9, 1.5) = (2.7, 4.6)
//       (8.9, 1.5) + (12.3, -1.4) = (21.2, 0.1)
//       (8.9, 1.5) + (-6.2, 3.1) = (2.7, 4.6)
//       (8.9, 1.5) + (8.9, 1.5) = (17.8, 3)

open System.Numerics

let values = [ Complex(12.3, -1.4); Complex(-6.2, 3.1); Complex(8.9, 1.5) ]

for c1 in values do
    for c2 in values do
        printfn $"{c1} + {c2} = {c1 + c2}"
// The example displays the following output:
//       (12.3, -1.4) + (12.3, -1.4) = (24.6, -2.8)
//       (12.3, -1.4) + (-6.2, 3.1) = (6.1, 1.7)
//       (12.3, -1.4) + (8.9, 1.5) = (21.2, 0.1)
//       (-6.2, 3.1) + (12.3, -1.4) = (6.1, 1.7)
//       (-6.2, 3.1) + (-6.2, 3.1) = (-12.4, 6.2)
//       (-6.2, 3.1) + (8.9, 1.5) = (2.7, 4.6)
//       (8.9, 1.5) + (12.3, -1.4) = (21.2, 0.1)
//       (8.9, 1.5) + (-6.2, 3.1) = (2.7, 4.6)
//       (8.9, 1.5) + (8.9, 1.5) = (17.8, 3)

Imports System.Numerics

Module modMain
   Public Sub Main()
      Dim values() As Complex = { New Complex(12.3, -1.4), 
                                  New Complex(-6.2, 3.1), 
                                  New Complex(8.9, 1.5) }   
      For Each c1 In values
         For Each c2 In values
            Console.WriteLine("{0} + {1} = {2}", c1, c2, c1 + c2)
         Next
      Next      
   End Sub
End Module
' The example displays the following output:
'       (12.3, -1.4) + (12.3, -1.4) = (24.6, -2.8)
'       (12.3, -1.4) + (-6.2, 3.1) = (6.1, 1.7)
'       (12.3, -1.4) + (8.9, 1.5) = (21.2, 0.1)
'       (-6.2, 3.1) + (12.3, -1.4) = (6.1, 1.7)
'       (-6.2, 3.1) + (-6.2, 3.1) = (-12.4, 6.2)
'       (-6.2, 3.1) + (8.9, 1.5) = (2.7, 4.6)
'       (8.9, 1.5) + (12.3, -1.4) = (21.2, 0.1)
'       (8.9, 1.5) + (-6.2, 3.1) = (2.7, 4.6)
'       (8.9, 1.5) + (8.9, 1.5) = (17.8, 3)

Remarks

The Addition operator allows performing addition operations that involve complex numbers. It enables code such as the following:

Complex c1 = new Complex(1.2, 2.3);
Complex c2 = new Complex(2.1, 3.2);
Complex c3 = c1 + c2;

let c1 = Complex(1.2, 2.3)
let c2 = Complex(2.1, 3.2)
let c3 = c1 + c2

Dim c1 As New Complex(1.2, 2.3)
Dim c2 As New Complex(2.1, 3.2)
Dim c3 As Complex = c1 + c2

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

Languages that don't support custom operators can call the Add equivalent group of methods instead.

The Addition operators that receive one double are more efficient than the operators that receive two Complex numbers.

Addition(Complex, Complex)

Source:

Complex.cs

Adds two complex numbers.

public:
 static System::Numerics::Complex operator +(System::Numerics::Complex left, System::Numerics::Complex right) = System::Numerics::IAdditionOperators<System::Numerics::Complex, System::Numerics::Complex, System::Numerics::Complex>::op_Addition;

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

static member ( + ) : System.Numerics.Complex * System.Numerics.Complex -> System.Numerics.Complex

Public Shared Operator + (left As Complex, right As Complex) As Complex

Parameters

left

Complex

The first complex value to add.

right

Complex

The second complex value to add.

Returns

Complex

The sum of left and right.

Implements

Addition(TSelf, TOther)

Remarks

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

$(a + c) + (b + d)i$

Languages that don't support custom operators can call the Complex.Add(Complex, Double) equivalent method instead.

See also

• Add(Complex, Complex)

Addition(Complex, Double)

Source:

Complex.cs

Adds a complex number to a double-precision real number.

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

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

static member ( + ) : System.Numerics.Complex * double -> System.Numerics.Complex

Public Shared Operator + (left As Complex, right As Double) As Complex

Parameters

left

Complex

The complex value to add.

right

Double

The double-precision real value to add.

Returns

Complex

The sum of left and right as a complex number.

Remarks

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

$(a + c) + bi$

Languages that don't support custom operators can call the Complex.Add(Double, Complex) equivalent method instead.

See also

• Add(Complex, Double)

Addition(Double, Complex)

Source:

Complex.cs

Adds a double-precision real number to a complex number.

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

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

static member ( + ) : double * System.Numerics.Complex -> System.Numerics.Complex

Public Shared Operator + (left As Double, right As Complex) As Complex

Parameters

left

Double

The double-precision real value to add.

right

Complex

The complex value to add.

Returns

Complex

The sum of left and right as a complex number.

Remarks

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

$(a + c) + di$

Languages that don't support custom operators can call the Complex.Add(Double, Complex) equivalent method instead.

See also

• Add(Double, Complex)