Chapter 14, Problem 10CR

To determine

To find:The correct option.

Answer to Problem 10CR

The correct answer is (b).

Explanation of Solution

Given:

  $-i$

Calculation:

The general form is,

  $z=r\left(\cos \theta +i\sin \theta \right)$

Calculate r.

  $\begin{array}{c}r=\sqrt{x^2+y^2}\\ =1\end{array}$

Calculate $z$

  $z=1\left(0+i\left(-1\right)\right)$

So,

  $\begin{array}{l}\cos \theta =1\\ \sin \theta =-1\end{array}$

Then,

  $\begin{array}{c}z=1\left(\cos 270+i\sin 270\right)\\ =\sqrt[n]{r}\left(\cos \frac{\theta +2\pi k}{n}+\sin \frac{\theta +2\pi k}{n}\right)\end{array}$

Solve the above for different values of k, then −i is not the cube root.

Thus, the correct answer is (b).