Hi all, sorry if this is the wrong section, wasn't sure if it would come under geometry.

The problem I have is to find the 3 roots of this equation:

$\displaystyle z^3 + 6z + 20 = 0$, given that $\displaystyle 1 + 3i$ is a root.

I solved this to get the 3 roots to be $\displaystyle 3 \pm i$ and $\displaystyle 2$.

It then ask you to plot the 3 roots on an Argand diagram and prove that the 3 points are vertices of a right angles triangle.

After plotting I found out the length of two of the sides, and using pythagoras showed that the length of the third was the root of the other two squared.

Just wondering if this is the correct way to do this, or if there is a 'proper' method that I should of used?

Thanks in advance

Craig