# equation complex number

posted by
**kevin** on
.

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..