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: 17



Work Step by Step

First, we use the division theorem to divide the absolute values and subtract the arguments: $\frac{4(\cos150^{\circ}+i\sin150^{\circ})}{2(\cos120^{\circ}+i\sin 120^{\circ})} \\=2(\cos (150^{\circ}-120^{\circ})+i\sin(150^{\circ}-120^{\circ})) \\=2(\cos30^{\circ}+i\sin30^{\circ})$ Since we know that $\cos30^{\circ}=\frac{\sqrt{3}}{2}$ and $\sin30^{\circ}=\frac{1}{2}$, we can substitute these values in the expression and simplify: $2(\cos30^{\circ}+i\sin30^{\circ}) \\=2(\frac{\sqrt{3}}{2}+\frac{1}{2}i) \\=\sqrt{3}+i$
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