Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 8 - Section 8.2 - Trigonometric Form for Complex Numbers - 8.2 Problem Set - Page 433: 49

Answer

$\color{blue}{9\ \text{cis}\ 180^\circ,\ 9\ \text{cis}\ \pi}$

Work Step by Step

$z=-9 = -9 +0i = x+iy \implies x=-9, y=0$ $\Huge\cdot$ modulus: $\quad r = \sqrt{x^2+y^2} = \sqrt{(-9)^2+0^2}= \sqrt{81} = 9$ $\Huge\cdot$ argument: $\quad \tan\theta=y/x=0/(-9)= 0;\ \cos\theta \lt 0 \implies \theta = 180^\circ \equiv \pi$ (smallest positive real angle $\theta$ from $+x$-axis to graph of $z$) $\begin{array}{|c|c|c|} \hline \text{Standard} & \text{Trigonometric} & \text{Trigonometric} \\ \text{Form} & \text{Form (deg)} & \text{Form (rad)} \\ \hline -9 & 9\ \text{cis}\ 180^\circ & 9\ \text{cis}\ \pi \\ \hline \end{array}$
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