Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.2 Trigonometric (Polar) Form of Complex Numbers - 8.2 Exercises - Page 364: 32

Answer

$\sqrt 3+i$

Work Step by Step

$2$ cis $30^{\circ}$=$2(\cos30^{\circ}+i\sin30^{\circ})$ It is known that $\cos30^{\circ}=\frac{\sqrt 3}{2}$ and $\sin30^{\circ}=\frac{1}{2}$ Substituting these values in the expression and solving: $2(\cos30^{\circ}+i\sin30^{\circ})=2(\frac{\sqrt 3}{2}+\frac{1}{2}i)=\sqrt 3+i$
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