Chapter 6.5, Problem 105E

To determine

To sketch:

The graph of the complex number satisfying the given condition

Explanation of Solution

Given:

The angle of complex number is

  $\theta =\frac{2\pi }{3}$

Concept used:

Definition of an nth root of a complex number:- The complex number $u=a+ib$ is an nth root of a complex number is $z$

  $\begin{array}{l}z=u^n\\ z={\left(a+ib\right)}^n\end{array}$

Calculation:

  $\theta =\frac{2\pi }{3}$

The standard form of complex number is

  $z=\left(x+iy\right)$

Test one point in each of the region formed by the graph

If the point satisfies the complex number then shade the entire region to denote that every point in the region satisfies the complex point

$x-axis$	$0$	$-0.5$	$-0.7$	$1$
$y-axis$	$0$	$0.866$	$0.71$	$0$