Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.2 Trigonometric (Polar) Form of Complex Numbers - 8.2 Exercises - Page 371: 37


$\frac{5}{2}-\frac{5\sqrt 3}{2}i$

Work Step by Step

$5$ cis $300^{\circ}$=$5(\cos300^{\circ}+i\sin300^{\circ})$ It is known that $\cos300^{\circ}=\frac{1}{2}$ and $\sin300^{\circ}=-\frac{\sqrt 3}{2}$ Substituting these values in the expression and solving: $5(\cos300^{\circ}+i\sin300^{\circ})=5(\frac{1}{2}-\frac{\sqrt 3}{2}i)=\frac{5}{2}-\frac{5\sqrt 3}{2}i$
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