Complex Numbers

A complex number is of the form:

where and . The complex number satisfies , the real number is called the real part of and is the imaginary part, and we write and . The polar form of a complex number is

where and . We visualize the set of complex numbers as a 2-dimensional real vector space:

complex plane.png

Definitions

Let and in polar form.

  1. The modulus of is .
  2. The angle (or argument) of is (or ).
  3. The conjugate of is .