Right triangle with complex vertices

[zelmac]

Homework Statement

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

Homework Equations

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]

These are the vertices of a right triangle in the complex plain right?
So this is basically a vector addition/subtraction problem.
Each side is the difference between two position vectors.

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