If z_{1} = x_{1} + iy_{1} and z_{2} = x_{2} + iy_{2} are two complex numbers then
 Addition
The real part is added separately and the complex part is added separately. z_{1} + z_{2} = (x_{1} + x_{2}) + i(y_{1} + y_{2})
 Subtraction
The real part is subtracted separately and the complex part is subtracted separately. z_{1}  z_{2} = (x_{1}  x_{2}) + i(y_{1}  y_{2})
 Multiplication
z_{1}×z_{2} = (x_{1}x_{2}  y_{1}y_{2}) + i(x_{1}y_{2} + x_{2}y_{1})
 Division
The denominator and numerator is multiplied by the complex conjugate of the denominator and the multiplication is carried out. The denominator left is the square of the modulus of the original denominator. z_{1}/z_{2} = [(x_{1}x_{2} + y_{1}y_{2}) + i(x_{2}y_{1}  x_{1}y_{2})]/(x_{2}^{2} + y_{2}^{2})
