Chapter 9.6, Problem 36E

To determine

To find: the rectangular form of the complex number and also graph the number.

Answer to Problem 36E

The rectangular form is $\left(\frac{\sqrt{3}}{2}-\frac{1}{2}i\right)$ .

Explanation of Solution

Given information: The complex number is $\left(\cos \left(-\frac{\pi }{6}\right)+i\sin \left(-\frac{\pi }{6}\right)\right)$ .

Calculation:

The rectangular form:

  $\begin{array}{l}\left(\cos \left(-\frac{\pi }{6}\right)+i\sin \left(-\frac{\pi }{6}\right)\right)\\ \Rightarrow 1\left(\frac{\sqrt{3}}{2}-i\frac{1}{2}\right)\\ \Rightarrow \left(\frac{\sqrt{3}}{2}-\frac{1}{2}i\right)\end{array}$

The graph will be: