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## Homework Statement

Find the geometric image of the complex number z, if [tex]z, z^2, z^3[/tex] are the vertices of a right triangle.

## Homework Equations

## The Attempt at a Solution

I tried expanding [itex]z^2, z^3[/itex], and than using both the pythagoras theorem, and vectors (in separate attempts), but failed to get at a solution.

All help is very appreciated :)