Definition

A complex number z can be expressed with
- the rectangular notation: z = x + iy

- the polar notation:

- the trigonometric form:

where x and y are real numbers and i is the imaginary unit, satisfying    = -1
The set of all complex numbers is denoted by C.

Operations With Complex Numbers

Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal. For any complex numbers a + bi and c + di, the following rules are true for the four basic operations. (a + bi) + (c + di) = (a + c) + (b + d )i
(a + bi) - (c + di) = (a - c) + (b - d )i
(a + bi)×(c + di) = (ac - bd )+ (ad + bc)i
a+bi =
c+di

The complex conjugate of the complex number 
The modulus of a complex number