find values of z given {(z+2i)^3}+i(3)^0.5?

Answer 1

let's suppose you are asking for

(z+2i)^3 = -i*sqrt(3)
The best way is to work in polar form
-i*sqrt3 = sqrt3 < 3pi/2+2kpi (< means angle) so z+2i = 3^(1/6) < pi/2 +2kpi/3 .You get different values giving k = 0,1,2.
I'll take the case k= 0

z+2i= 3^1/6 i ( passed a binomial)
so z = (3^1/6-2)*i
k=1 z+2i= -sqrt3 /2 -1/2i so z = -sqrt3 /2-5/2i

You can do the case k=2

Answer 2

question doesnt make sense. you need an equal sign. also the second part looks ambiguous with bracketing.