Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix G - Complex Numbers - G Exercises - Page A56: 28


$8(\displaystyle \cos\frac{\pi}{2}+i\sin\frac{\pi}{2})$

Work Step by Step

We are given: $z=8i=0+8i$ To find $r$ of a complex number $a+bi$, we use: $\sqrt{a^2+b^2}$: $r=\sqrt{0^{2}+8^{2}}=8$ To find $\theta$, we use $\tan{\theta}=\frac{b}{a}$: $\displaystyle \tan\theta=\frac{8}{0}$=undefined (or +$\infty$) And since $z$ is located at (0,8) (y-axis), we have: $\displaystyle \theta=\frac{\pi}{2}$ To put the number in polar form, we use $r(\cos{\theta}+i\sin{\theta})$: $8(\displaystyle \cos\frac{\pi}{2}+i\sin\frac{\pi}{2})$
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