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: 48

Answer

$\color{blue}{8\ \text{cis}\ 90^\circ,\ 8\ \text{cis}\ \pi/2}$

Work Step by Step

$z=8i = 0 +8i = x+iy \implies x=0, y=8$ $\Huge\cdot$ modulus: $\quad r = \sqrt{x^2+y^2} = \sqrt{0^2+8^2}= \sqrt{64} = 8$ $\Huge\cdot$ argument: $\quad \tan\theta=y/x=8/0,\ \text{DNE};\ \sin\theta \gt 0 \implies \theta = 90^\circ \equiv \pi/2$ (smallest positive real angle $\theta$ from $+x$-axis to graph of $z$) $\begin{array}{|c|c|c|} \hline \text{Standard} & \text{Trigonometric} & \text{Trigonometric} \\ \text{Form} & \text{Form (deg)} & \text{Form (rad)} \\ \hline 8i & 8\ \text{cis}\ 90^\circ & 8\ \text{cis}\ \pi/2 \\ \hline \end{array}$
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