Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 799: 59

Answer

Step 1. See figure. Step 2. $5cos(233^\circ)+5i\ sin(233^\circ)$
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Work Step by Step

Step 1. Given the complex number $-3-4i$, we can identify $a=-3, b=-4$ as $(-3,-4)$ in complex coordinates as shown in the figure. Step 2. Using the above results, we can get the modulus as $r=\sqrt {a^2+b^2}=\sqrt {(-3)^2+(-4)^2}=5$. The polar angle can be found as $tan\theta=\frac{b}{a}=\frac{-4}{-3}=\frac{4}{3}$ which gives $\theta=180^\circ +tan^{-1}(\frac{4}{3})\approx180^\circ +53^\circ =233^\circ $ (in quadrant III). Thus, we can write the complex number in polar form as $-3-4i=5cos(233^\circ)+5i\ sin(233^\circ)$
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