# Section 4.4 Polar Form of a Complex Number

**Section Objectives**

- Write complex numbers in polar (trigonometric) form.
- 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 .