Which of the following is a fourth root of 1 ?
I. $\cos \left( \frac { 3 \pi } { 2 } \right) + i \sin \left( \frac { 3 \pi } { 2 } \right)$
II. $\frac { 1 } { 4 } ( \cos ( 0 ) + i \sin ( 0 ) )$
III. $\cos \left( \frac { \pi } { 4 } \right) + i \sin \left( \frac { \pi } { 4 } \right)$
A) None are roots.
B) II and III are the only roots.
C) I and II are the only roots.
D) I, II, and III are roots.
E) I is the only root.

Question

Quizplus · Accepted Answer

I is a fourth root of 1 because it represents $e^{i\frac{3\pi}{2}}$, which raised to the fourth power equals 1. II is not a root because it's a fraction and not in the form of $e^{ix}$. III is not a fourth root of 1 because $e^{i\frac{\pi}{4}}$ raised to the fourth power equals $i$, not 1.

Which of the Following Is a Fourth Root of 1 cos⁡(3π2)+isin⁡(3π2)\cos \left( \frac { 3 \pi } { 2 } \right) + i \sin \left( \frac { 3 \pi } { 2 } \right)cos(23π​)+isin(23π​)

Which of the Following Is a Fourth Root of 1 $\cos \left( \frac { 3 \pi } { 2 } \right) + i \sin \left( \frac { 3 \pi } { 2 } \right)$