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 8.3 The Product and Quotient Theorems - 8.3 Exercises - Page 376: 23

Answer

$\frac{8}{\sqrt{3}+i}$ = $2\sqrt{3} - 2i$

Work Step by Step

$\frac{8}{\sqrt{3}+i}$ = $\frac{8cis0^\circ}{2cis30^\circ}$ = $4cis(0-30)^\circ$ = $4\cdot cos(-30^\circ) + 4i\cdot sin(-30^\circ)$ = $4\cdot \frac{\sqrt{3}}{2} - 4i\cdot \frac{1}{2}$ = $2\sqrt{3} - 2i$
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