- #1

Darkmisc

- 163

- 23

- Homework Statement:
- z^3+8i=0

- Relevant Equations:
- r^3cis3t = 8cis(-pi/2)

Hi everyone

How do you know how many solutions z has

a) in this problem

b) in general?

I understand that they are rotating 2 pi from (-pi/2) in both directions to get the other two solutions. Should this be done in all problems?

Is it simply a coincidence that there are three solutions when z is in the third power?

If the problem needed to be solved for z^4, would there be four solutions? Or only three (again by rotating 2 pi in both directions)?

Thanks

How do you know how many solutions z has

a) in this problem

b) in general?

I understand that they are rotating 2 pi from (-pi/2) in both directions to get the other two solutions. Should this be done in all problems?

Is it simply a coincidence that there are three solutions when z is in the third power?

If the problem needed to be solved for z^4, would there be four solutions? Or only three (again by rotating 2 pi in both directions)?

Thanks