Question

True or False

The polar form of a nonzero complex number is unique.

Short answer

Given statement is true.

Step-by-step solution

Step 1. Given information

A statement is given as The polar form of a nonzero complex number is unique.

Step 2. Explanation

While we convert into polar form, there are two things radius and angle.

Radius of different form may be same but angle is unique for a complex number.

Consider complex number as,

$z=x+iy$

Now the angle is

$$\begin{gathered} \theta ={\cos }^{-1}\left(\frac{x}{r}\right) \\ ={\sin }^{-1}\left(\frac{y}{r}\right) \\ ={\tan }^{-1}\left(\frac{y}{x}\right) \end{gathered}$$

Angle is unique, hence given statement is true.