A complex number can be expressed as:
where is the imaginary unit. Both and are real numbers. They are called the real and imaginary parts of , respectively.
The complex number can also be expressed in exponential and polar forms:
In the above equations, is called the modulus of and is the argument or phase angle of . It can easily be shown that:
The complex conjugates will not affect common operators:
De Moivre's Theorem:
Roots of Complex Numbers:
where is an integer.