Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.3 The Product and Quotient Theorems - 8.3 Exercises - Page 370: 34

Answer

$w = \sqrt{2}(cos135^\circ + isin135^\circ)$ $z = \sqrt{2}(cos225^\circ + isin225^\circ)$

Work Step by Step

$w = -1 + i$ is at $135^\circ$ with absolute value $\sqrt{(-1)^2 + 1^2} = \sqrt{2}$, hence, the trigonometric form of $w$ is $\sqrt{2}cis135^\circ$, and in equivalent form it will be, $w = \sqrt{2}(cos135^\circ + isin135^\circ)$ whereas, $z = -1 - i$ is at $225^\circ$ with absolute value $\sqrt{(-1)^2 + (-1)^2} = \sqrt{2}$, hence, the trigonometric form of $z$ is $\sqrt{2}cis225^\circ$, and in equivalent form it will be, $z = \sqrt{2}(cos225^\circ + isin225^\circ)$
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