Question

solve z^3=27i
with explanation please

Answer 1

z^3 = - 27i^3
z^3 + (3i)^3 = 0 => (z +3i)( z^2 +9i^2 - 3zi) = 0
Now solve for z

Answer 2

how did u get the third step??

Answer 3

Couldn't you also just take cube-root of both sides since both sides are perfect cubes?

Answer 4

a3 + b^3 = (a+b)(a^2 + b^2 -ab)

Answer 5

ok ty :)

Answer 6

we need three roots here not one as it is z^3 @cliffedge

Answer 7

Ah, true..
z^3 = (-3)^3*(i)^3
-> z = -3i
Only finds one.
I was actually first considering DeMoivre's Formula.
That should work here, right?

Answer 8

Not sure but you can try it if you want