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: 35

Answer

$w\cdot z$ = $2$

Work Step by Step

For $w$, the trigonometric form of it is $\sqrt{2}cis135^\circ$ whereas, for $z$, the trigonometric form of it is $\sqrt{2}cis225^\circ$ The product of $w$ and $z$ will be $w\cdot z$ = $\sqrt{2}cis135^\circ\cdot$ $\sqrt{2}cis225^\circ$ = $(\sqrt{2})^2 cis(135^\circ + 225^\circ)$ (Product Theorem) = $2 cis360^\circ$ = $2 (1 + 0i)$ = $2$
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