Chapter 6.6, Problem 65E

Solution

To check: Whether the statement is true or false.

The statement is false.

Given information:

The given statement is "The polar form of a complex number is unique".

Explanation:

The polar form of a complex number $z=a+bi$ is given by,

  $z=r\left(\cos \theta +i\sin \theta \right)$

The above polar form can also be written as follows.

  $z=r\left[\cos \left(\theta +2\pi n\right)+i\sin \left(\theta +2\pi n\right)\right]$

So, the polar form of a complex number is not unique.

Therefore, the statement is false.