anybody with any idea please help!!!

i have 3 questions if anyone can help it would be greatly appreciated.

1) Have to use de Moivre's theorem to calculate

(1+√3i)3 / (1-i) 4

Expressing the answer in z=a+bi form.

I have found both the polar forms for them which could possibly be wrong, its just that get confused when i convert it to a cartesian. I need to calrify my first answer and see how to do it correctly!

2) If z= cosŲ + i sinŲ, show that

cos nŲ = ½ (zn + 1/n)

sin nŲ = ½i (zn + 1/zn)

3) Prove that sin5Ų + sinŲ = 2 sin 3Ų cosŲ

with the other two question, i pretty much don't have a clue on what to do!!!