Section 4.4 Polar Form of a Complex Number

Section Objectives

  1. Write complex numbers in polar (trigonometric) form.
  2. Multiply and divide complex numbers in polar form.



Polar or Trigonometric Form

The polar (or trigonometric) form of the complex number is

,

where and . is the absolute value (or modulus) of , and is called the argument of . Normally, is restricted so that .



Examples










Multiplication and Division in Polar Form

It is fairly easy to prove the following useful results.


Let and .