Solving Complex Number Question z^3+i=0 using z^n=|z|^(n) x e^((i)(n)(theta))

[Ry122]

Find z
Question:
z^3+i=0
My attempt:
z^3=-i
use z^n=|z|^(n) x e^((i)(n)(theta))
n = 3
|z|=1
theta = -pie/2
Is this correct?

 

[transgalactic]

if z=i

z^2=-1 z^3=-1*i >>-i

 

[tiny-tim]

… one step at a time …

z^3+i=0
My attempt:
z^3=-i
use z^n=|z|^(n) x e^((i)(n)(theta))

Hi Ry122!

You must be much more logical, or you'll make mistakes.

Do it one step at a time.

You know z^3=-i.

So - first step - write -i in the form r.e^(i theta).

What is it?

Then divide theta by 3.

Oh … and how many different solutions are there?