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
i² = -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