SOLUTION: Find the solution to the equation (z^2-2)(z^3+i)=0

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Question 945089: Find the solution to the equation
(z^2-2)(z^3+i)=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28z%5E2-2%29%28z%5E3%2Bi%29=0
You can both terms further,
%28z-sqrt%282%29%29%28z%2Bsqrt%282%29%29%28z-i%29%28z%5E2%2Biz-1%29=0
So then,
z-sqrt%282%29=0
highlight%28z=sqrt%282%29%29
.
.
z%2Bsqrt%282%29=0
highlight%28z=-sqrt%282%29%29
.
.
z-i=0
highlight%28z=i%29
.
.
Complete the square for the final term,
z%5E2%2Biz-1=0
z%5E2%2Biz%2B%28i%2F2%29%5E2-1=%28i%5E2%2F2%29
%28z%2Bi%2F2%29%5E2=-1%2F4%2B1
%28z%2Bi%2F2%29%5E2=3%2F4
z%2Bi%2F2=0+%2B-+sqrt%283%29%2F2
highlight%28z=-i%2F2+%2B-+sqrt%283%29%2F2%29