Complex Operations and Conjugates
Complex numbers are binomials of a sort - They can be added, subtracted, and multiplied in a similar way, however division is a little different.

Complex addition
(a+bi) + (c+di) = (a+c) + i(b+d)

Complex subtraction
(a+bi) - (c+di) = (a-c) + i(b-d)

Complex multiplication
(a+bi)(c+di) = (ac-bd) + i(ad+bc)

To do (a+bi)/(c=di) you use the complex conjugate...
A conjugate is where the sign in the middle is changed like this:

Complex division
Multiply both the numerator and the denominator by the conjugate of the denominator and you get:
(a+bi) / (c+di) = ((ac+bd) + i(bc-ad))/ (c² + d²)

The complex conjugate of z is often written with a bar over the top:

If z = x + iy, then the complex conjugate of z is expressed as z = x - iy.

z + z = 2x

z - z = 2iy

A complex number is real if and only if z = z.

A complex number is imaginary if and only if z = -z.

Try out this online Complex Number Calculator
To see more on operations of complex numbers, visit: Complex Numbers and Operations