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# Complex.Equals Method (Complex)

Visual Studio 2010

Returns a value that indicates whether the current instance and a specified complex number have the same value.

Namespace:  System.Numerics
Assembly:  System.Numerics (in System.Numerics.dll)

## Syntax

```'Declaration
Public Function Equals ( _
value As Complex _
) As Boolean
```

#### Parameters

value
Type: System.Numerics.Complex
The complex number to compare.

#### Return Value

Type: System.Boolean
true if this complex number and value have the same value; otherwise, false.

#### Implements

IEquatable(Of T).Equals(T)

## Remarks

The Equals(Complex) method provides the IEquatable(Of T) implementation for the Complex structure. It performs slightly better than Equals(Object) method because it does not have to convert its parameter to a complex number.

Two complex numbers are equal if their real parts are equal and their imaginary parts are equal. The Equals(Complex) method is equivalent to the following expression:

```
Return Me.Real.Equals(value.Real) AndAlso Me.Imaginary.Equals(value.Imaginary)

```

Notes to Callers

Use the Equals method with caution, because two values that are apparently equivalent can be considered unequal due to the differing precision of their real and imaginary components. The following example reports that (3.33333, 0.142857) and (10/3, 1/7) are not equal.

```
Dim c1 As New System.Numerics.Complex(3.33333, .142857)
Dim c2 As New System.Numerics.Complex(10/3, 1/7)
Console.WriteLine("{0} = {1}: {2}", c1, c2, c1.Equals(c2))
' The example displays the following output:
'    (3.33333, 0.142857) = (3.33333333333333, 0.142857142857143): False

```

One recommended technique is to define an acceptable margin of difference between the two values (such as .01% of one of the values' real and imaginary components) instead of comparing the values for equality. If the absolute value of the difference between the two values is less than or equal to that margin, the difference is likely to be due to a difference in precision, and, therefore, the values are likely to be equal. The following example uses this technique to compare the two complex values that the previous code example found to be unequal. It finds the two complex numbers to be equal.

```
Dim c1 As New System.Numerics.Complex(3.33333, .142857)
Dim c2 As New System.Numerics.Complex(10/3.0, 1.0/7)
Dim difference As Double = .0001

' Compare the values
Dim result As Boolean = (Math.Abs(c1.Real - c2.Real) <= c1.Real * difference) And
(Math.Abs(c1.Imaginary - c2.Imaginary) <= c1.Imaginary * difference)
Console.WriteLine("{0} = {1}: {2}", c1, c2, result)
' The example displays the following output:
'    (3.33333, 0.142857) = (3.33333333333333, 0.142857142857143): True

```

Supported in: 4

Supported in: 4

## Platforms

Windows 7, Windows Vista SP1 or later, Windows XP SP3, Windows Server 2008 (Server Core not supported), Windows Server 2008 R2 (Server Core supported with SP1 or later), Windows Server 2003 SP2

The .NET Framework does not support all versions of every platform. For a list of the supported versions, see .NET Framework System Requirements.