Chapter 9, Problem 51SGA

To determine

To graph: the complex number and then express it in rectangular form.

Answer to Problem 51SGA

  $\sqrt{3}+i$

Explanation of Solution

Given information:

  $2\left(\cos \frac{\pi }{6}+i\sin \frac{\pi }{6}\right)$

Calculation:

Use the graphing calculator to graph the given complex as shown below.

  

Now solve the given expression to evaluate the rectangular form as shown below.

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

Thus the rectangular form of the given complex number is $\sqrt{3}+i$ .