SOLUTION: A solution for z^3 + 2 + 2root3i = 0 1) 2^2/3(cos4pi/9 + i.sin 4pi/9) 2) 4^1/4(cos11pi/12 + i.sin11pi/12) 3) 2^2/3(cos 17pi/12 + i.sin17pi/12) 4) 4^1/3(cos7pi/6 + i.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: A solution for z^3 + 2 + 2root3i = 0 1) 2^2/3(cos4pi/9 + i.sin 4pi/9) 2) 4^1/4(cos11pi/12 + i.sin11pi/12) 3) 2^2/3(cos 17pi/12 + i.sin17pi/12) 4) 4^1/3(cos7pi/6 + i.      Log On


   

Question 1157653: A solution for z^3 + 2 + 2root3i = 0
1) 2^2/3(cos4pi/9 + i.sin 4pi/9)
2) 4^1/4(cos11pi/12 + i.sin11pi/12)
3) 2^2/3(cos 17pi/12 + i.sin17pi/12)
4) 4^1/3(cos7pi/6 + i.sin7pi/6)
5) 2^2/3(cos11pi/12 + i.sin 11pi/12)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Use deMoivre's Theorem.

z%5E3%2B2%2B2i%2Asqrt%283%29+=+0

z%5E3+=+-2-2i%2Asqrt%283%29+=+4cis%284pi%2F3%29

z+=+%284cis%284pi%2F3%29%29%5E%281%2F3%29+=+%284%5E%281%2F3%29%29%28cis%284pi%2F9%29%29

That is equivalent to answer 1.

ANSWER: 1) 2^2/3(cos4pi/9 + i.sin 4pi/9