Complex numbers question (1 Viewer)

girrawhat · Aug 5, 2012

I seemed to have completely forget the basics of complex numbers. Could someone help explain this question
to me

Given z^5=i

Solve for z and graph on argand plane

I just need help solving for z

unLimitieDx · Aug 5, 2012

De Moivre's theorem

r^5 cis5O = cis pie/2

girrawhat · Aug 5, 2012

Could u please show full answer pls. I think I forgot how to use the 2k pi

rolpsy · Aug 5, 2012

$\begin{align*}z^5 &= i\\&= \text{cis} \left ( \frac{\pi}{2} \right )\\&= \text{cis} \left ( \frac{\pi}{2} + 2k\pi \right )&&&k\in\mathbb{Z}\\z&=\text{cis} \left ( \frac{\pi}{2} + 2k\pi \right )^{\frac{1}{5}}\\&=\text{cis} \left ( \frac{\pi}{10} + \frac{2k\pi}{5} \right )\\\end{align*}$

Letting k = -2, -1, 0, 1, 2:

$z = \text{cis}\left ( -\frac{7\pi}{10} \right ), \text{cis}\left ( -\frac{3\pi}{10} \right ), \text{cis}\left ( \frac{\pi}{10} \right ), \text{cis}\left ( \frac{\pi}{2} \right ), \text{cis}\left ( \frac{9\pi}{10} \right )$

asianese · Aug 5, 2012

Note that the syllabus only requires roots of 'unity' which are + or - 1.

girrawhat · Aug 5, 2012

thankyou. much appreciated

girrawhat · Aug 5, 2012

asianese said:
Note that the syllabus only requires roots of 'unity' which are + or - 1.

Only unity? Every test, we had at our school there was a question like this

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Complex numbers question (1 Viewer)

girrawhat

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