Answer
$$z=5i$$
Work Step by Step
$$5 \left ( \cos \frac{\pi }{2}+i \sin \frac{\pi }{2} \right )= 5 (0+i)=5i$$So the rectangular form of the complex number $5 \left ( \cos \frac{\pi }{2}+i \sin \frac{\pi }{2} \right )$ is$$z=5i.$$
Precalculus (6th Edition) Blitzer
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13446-914-3
ISBN 13:
978-0-13446-914-0
Chapter 6 - Section 6.5 - Complex Numbers in Polar Form; DeMoivre's Theorem - Exercise Set - Page 767: 33
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