Complex numbers Questions

Hi,

I have recently started doing a further maths "a level" course, and im having a bit of diffuculty with some of the harder complex numbr questions.

The last two i have been working on for hours, but I just cant seem to get them, its probably something simple but anyway;

1. given that a and b are real constants, prove that "ai" is a root of the equation;

z³-bz² +a²z- a²b=0

and find the roots of the equation in terms of a and b.

2. Simplify without the use of a calculator:

(cos π/7 -i sin π/7)/(cos π/7 + i sin π/7)

I have tried these many times but to no avail. Thanks for your help(Rofl),

Owen.