# Right triangle with complex vertices

## Homework Statement

Find the geometric image of the complex number z, if $$z, z^2, z^3$$ are the vertices of a right triangle.

## The Attempt at a Solution

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

All help is very appreciated :)

Simon Bridge
Figure out which is the hypotenuse and then you need only set the angle between the other two sides to $\pi/2$.