# Complex.Equals Method (Object)

**.NET Framework 4.6 and 4.5**

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

**Namespace:**System.Numerics

**Assemblies:**System.Runtime.Numerics (in System.Runtime.Numerics.dll)

System.Numerics (in System.Numerics.dll)

#### Parameters

- obj
- Type: System.Object
The object to compare.

#### Return Value

Type: System.Booleantrue 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.

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:

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.

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.

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

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