Chapter 6.6, Problem 140E

a.

To determine

To find: how many roots are not shown.

Answer to Problem 140E

3 roots not shown.

Explanation of Solution

Given information: The figure shows one of the forth roots of a complex number z .

  

Calculation:

Since there are four roots & one is shown, then there are 3 roots not shown.

b.

To determine

To describe: the other roots.

Explanation of Solution

The roots are $\frac{{360}^{\circ }}{n}$ apart where n = 4 (number of roots).

So that the other roots lie on the circle. Starting from the root shown add ${90}^{\circ }$ to find the second , then add another ${90}^{\circ }$ to find the third and finally add the last ${90}^{\circ }$ to find the fourth root.