Homework Help: equation complex number

Posted by kevin on Friday, November 3, 2006 at 8:24pm.

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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