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 432: 42

Answer

$\color{blue}{\sqrt{2}\ \text{cis}\ 45^\circ, \sqrt{2}\ \text{cis}\ \pi/4}$

Work Step by Step

$z=1+i = x+iy \implies x=1, y=1$ $\Huge\cdot$ modulus: $\quad r = \sqrt{x^2+y^2} = \sqrt{1^2+1^2}=\sqrt{2}$ $\Huge\cdot$ argument: $\quad \tan\theta = y/x=1/1=1 \implies \theta = 45^\circ \equiv \pi/4$ (smallest positive real angle $\theta$ from $+x$-axis to graph of $z$) $\begin{array}{|c|c|c|} \hline \text{Standard} & \text{Trigonometric} & \text{Trigonometric} \\ \text{Form} & \text{Form (deg)} & \text{Form (rad)} \\ \hline 1+i & \sqrt{2}\ \text{cis}\ 45^\circ & \sqrt{2}\ \text{cis}\ \pi/4 \\ \hline \end{array}$
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