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,