z^4 + 81 = 0 (solve)
change it to polar, then take the root.
z^4= 81@180
z= 3@180/4 + n90 where n=0, 1, 2, 3
check:
z= 3@180/4 + 3*90=3@315
z^4=81@(4*315)=81@1260= 91@180=81
you can check it at the other roots also.
this is what i did:
z^4 =  81
z (81 cis 180)^1/4
81 ^ 1/4 cis 1/4 * 180
3 cis 45 therefore 360/4 = 90*
4 solutions:
3 cis 45*
3 cis 135*
3 cis  135*
3 cis  45*
???
That is it. You get four roots, the same as mine. I did not use positive and negative angles, just positive. That is a preference I have. It is easier for me to think of rotation in one direct, so your 45 is 315 for me.
thanks for the help, a bit confusing trying to read explanations for maths over the internet but hey we got the right answers. :)
It does take a while to understand the ASCII labels for math. Fractions are the most difficult..
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