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## Homework Statement

Let [tex]z=|z|e^{\alpha*i}[/tex]

Using the fact that [tex]z*w=|z||w|e^{i(\alpha+\beta)}[/tex], find all solutions to

[tex]z^4 = -1[/tex]

## The Attempt at a Solution

Not quite sure how to proceed, except for the obvious step

[tex]i=z^2=|z*z|e^{i(2\alpha)}= |z*z|[cos(2\alpha)+isin(2\alpha)][/tex]

Kinda stuck here :s any hints? Thanks.