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# Complex.Equals Method (Object)

Visual Studio 2010

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

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

## Syntax

```'Declaration
Public Overrides Function Equals ( _
obj As Object _
) As Boolean
```

#### Parameters

obj
Type: System.Object
The object to compare.

#### Return Value

Type: System.Boolean
true if the obj parameter is a Complex object or a type capable of implicit conversion to a Complex object, and its value is equal to the current Complex object; otherwise, false.

## Remarks

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

```
Return Me.Real.Equals(CType(value, Complex).Real) AndAlso
Me.Imaginary.Equals(CType(value, Complex).Imaginary)

```

If the obj parameter is not a Complex object, but it is a data type for which an implicit conversion is defined, the Equals(Object) method converts obj to a Complex object whose real part is equal to the value of obj and whose imaginary part is equal to zero before it performs the comparison. The following example illustrates this by finding that a complex number and a double-precision floating-point value are equal.

```
Dim n1 As Double = 16.33
Dim c1 As New System.Numerics.Complex(16.33, 0)
Console.WriteLine(c1.Equals(n1))                ' Returns True.

```

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 problem can be accentuated if obj must be converted to a Double before performing the comparison. The following example compares a complex number whose real component appears to be equal to a Single value with that Single value. As the output shows, the comparison for equality returns False.

```
Imports System.Numerics

Module Example
Public Sub Main()
Dim n1 As Single = 1.430718e-12
Dim c1 As New Complex(1.430718e-12, 0)
Console.WriteLine("{0} = {1}: {2}", c1, n1, c1.Equals(n1))
End Sub
End Module
' The example displays the following output:
'       (1.430718E-12, 0) = 1.430718E-12: 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 values that the previous code example found to be unequal. It now finds them to be equal.

```
Imports System.Numerics

Module Example
Public Sub Main()
Dim n1 As Single = 1.430718e-12
Dim c1 As New Complex(1.430718e-12, 0)
Dim difference As Double = .0001

' Compare the values
Dim result As Boolean = (Math.Abs(c1.Real - n1) <= c1.Real * difference) And
c1.Imaginary = 0
Console.WriteLine("{0} = {1}: {2}", c1, n1, result)
End Sub
End Module
' The example displays the following output:
'       (1.430718E-12, 0) = 1.430718E-12: 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.