Overloadable Operators C# with Example

C# allows user-defined types to overload operators by defining static member functions using the operator 
keyword. 
The following example illustrates an implementation of the + operator. 
If we have a Complex class which represents a complex number: 
public struct Complex 
{ 
public double Real { get; set; } 
public double Imaginary { get; set; } 
} 
And we want to add the option to use the + operator for this class. i.e.: 
Complex a = new Complex() { Real = 1, Imaginary = 2 }; 
Complex b = new Complex() { Real = 4, Imaginary = 8 }; 
Complex c = a + b; 
We will need to overload the + operator for the class. This is done using a static function and the operator keyword: 
public static Complex operator +(Complex c1, Complex c2) 
{ 
return new Complex 
{ 
Real = c1.Real + c2.Real, 
Imaginary = c1.Imaginary + c2.Imaginary 
}; 
} 
Operators such as +, -, *, / can all be overloaded. This also includes Operators that don't return the same type (for 
example, == and != can be overloaded, despite returning booleans) The rule below relating to pairs is also enforced 
here. 
Comparison operators have to be overloaded in pairs (e.g. if < is overloaded, > also needs to be overloaded). 
A full list of overloadable operators (as well as non-overloadable operators and the restrictions placed on some 
overloadable operators) can be seen at MSDN - Overloadable Operators (C# Programming Guide). 
 

Version ≥ 7.0 
overloading of operator is was introduced with the pattern matching mechanism of C# 7.0. For details see Pattern 
Matching 
Given a type Cartesian defined as follows 
public class Cartesian 
{ 
public int X { get; } 
public int Y { get; } 
} 
An overloadable operator is could e.g. be defined for Polar coordinates 
public static class Polar 
{ 
public static bool operator is(Cartesian c, out double R, out double Theta) 
{ 
R = Math.Sqrt(c.X*c.X + c.Y*c.Y); 
Theta = Math.Atan2(c.Y, c.X); 
return c.X != 0 || c.Y != 0; 
} 
} 
which can be used like this 
var c = Cartesian(3, 4); 
if (c is Polar(var R, *)) 
{ 
Console.WriteLine(R); 
} 
(The example is taken from the Roslyn Pattern Matching Documentation)