find all roots of z^5-1-j=0 and plot on a complex plane
what is even the working to this?

Question

find all roots of z^5-1-j=0 and plot on a complex plane
what is even the working to this?

anonymous · Answer

Whats is j? General quintic equations can't be solved in terms of elementary functions.

anonymous · Answer

j is the square root of -1
i should get into the habit of typing it as i actually

anonymous · Answer

lol your used to using i to denote current?

anonymous · Answer

yeah my uni has very unorthodox way of teaching

anonymous · Answer

Here are all 5 solutions, along with an argand diagram plotting them

anonymous · Answer

http://www.wolframalpha.com/input/?i=z%5E5-1%3Di

nikvist · Answer

$$z^5-1-i=0$$$$z^5=1+i=\sqrt{2}\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}i\right)=\sqrt{2}\exp\left(\frac{\pi}{4}+2\pi k\right),k=0,\dots,4$$$$z=\sqrt[10]{2}\exp\left(\frac{\pi}{20}+\frac{2\pi}{5} k\right),k=0,\dots,4$$

nikvist · Answer

I dont understand your question Loser66.

loser66 · Answer

never mind, I got it. thanks for response