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: 57

Answer

Step 1. See figure. Step 2. $\sqrt 2cos(\frac{7\pi}{4})+i\sqrt 2sin(\frac{7\pi}{4})$
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Work Step by Step

Step 1. Given the complex number $1-i$, we can identify $a=1, b=-1$ given $(1,-1)$ in complex coordinates as shown in the figure. Step 2. Using the above results, we can get the modulus as $r=\sqrt {a^2+b^2}=\sqrt {1^2+(-1)^2}=\sqrt 2$. The polar angle can be found as $tan\theta=\frac{b}{a}=-1$, which gives $\theta=\frac{7\pi}{4}$ (in quadrant IV). Thus, we can write the complex number in polar form as $1-i=\sqrt 2cos(\frac{7\pi}{4})+i\sqrt 2sin(\frac{7\pi}{4})$
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