# Complex.Equals Method

## Definition

Returns a value that indicates whether two complex numbers are equal.

 Equals(Complex) Returns a value that indicates whether the current instance and a specified complex number have the same value. Equals(Object) Returns a value that indicates whether the current instance and a specified object have the same value.

## Equals(Complex)

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

``````public:
virtual bool Equals(System::Numerics::Complex value);``````
``public bool Equals (System.Numerics.Complex value);``
``override this.Equals : System.Numerics.Complex -> bool``
``Public Function Equals (value As Complex) As Boolean``

#### Parameters

value
Complex

The complex number to compare.

#### Returns

Boolean

`true` if this complex number and `value` have the same value; otherwise, `false`.

### Remarks

The Equals(Complex) method provides the IEquatable<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 this.Real.Equals(value) && this.Imaginary.Equals(value);
``````
``````Return Me.Real.Equals(value.Real) AndAlso Me.Imaginary.Equals(value.Imaginary)
``````

### Notes to Callers

Use the Equals(Complex) 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.

``````System.Numerics.Complex c1 = new System.Numerics.Complex(3.33333, .142857);
System.Numerics.Complex c2 = new System.Numerics.Complex(10/3.0, 1.0/7);
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
``````
``````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.

``````System.Numerics.Complex c1 = new System.Numerics.Complex(3.33333, .142857);
System.Numerics.Complex c2 = new System.Numerics.Complex(10/3.0, 1.0/7);
double difference = .0001;

// Compare the values
bool result = (Math.Abs(c1.Real - c2.Real) <= c1.Real * difference) &
(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
``````
``````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
``````

## Equals(Object)

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

``````public:
override bool Equals(System::Object ^ obj);``````
``public override bool Equals (object obj);``
``override this.Equals : obj -> bool``
``Public Overrides Function Equals (obj As Object) As Boolean``

#### Parameters

obj
Object

The object to compare.

#### Returns

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 this.Real.Equals(((Complex) value).Real) &&
this.Imaginary.Equals(((Complex) value).Imaginary);
``````
``````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.

``````double n1 = 16.33;
System.Numerics.Complex c1 =
new System.Numerics.Complex(16.33, 0);
Console.WriteLine(c1.Equals(n1));               // Returns true.
``````
``````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(Complex) 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`.

``````using System;
using System.Numerics;

public class Example
{
public static void Main()
{
float n1 = 1.430718e-12f;
Complex c1 = new Complex(1.430718e-12, 0);
Console.WriteLine("{0} = {1}: {2}", c1, n1, c1.Equals(n1));
}
}
// The example displays the following output:
//       (1.430718E-12, 0) = 1.430718E-12: 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.

``````using System.Numerics;

public class Example
{
public static void Main()
{
float n1 = 1.430718e-12f;
Complex c1 = new Complex(1.430718e-12, 0);
double difference = .0001;

// Compare the values
bool result = (Math.Abs(c1.Real - n1) <= c1.Real * difference) &
c1.Imaginary == 0;
Console.WriteLine("{0} = {1}: {2}", c1, n1, result);
}
}
// The example displays the following output:
//       (1.430718E-12, 0) = 1.430718E-12: True
``````
``````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
``````