Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 8 - Quiz (Sections 8.1-8.4) - Page 385: 3a

Answer

$(1 - i)^3$ = $- 2 - 2i$

Work Step by Step

$1 - i$ is at $315^\circ$ with absolute value $\sqrt{(1)^2 + (-1)^2} = \sqrt{2}$, the equivalent trigonometric form of $ 1 - i$ is $\sqrt{2}cis315^\circ$. $(1 - i)^3$ = $(\sqrt{2}cis315^\circ)^3$ = $(\sqrt{2})^3cis3\cdot 315^\circ$ (De Moivre’s theorem) = $(\sqrt{2})^3cis945^\circ$ = $(\sqrt{2})^3cis225^\circ$ ($945^\circ$ and $225^\circ$ are coterminal) = $(\sqrt{2})^3 (- \frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}}i)$ = $- 2 - 2i$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.