Hi this is about complex numbers and I apologize if it doesn't fall under this thread!

I really need help with this one, I really can't figure it out. Its just one question but there's a lot to refer to from previous parts, I know it taxing and I would appreciate your help so so much!

Use the results of ___________ to prove

Now

_______ will refer to the previous parts of this question, ( I don't know which part will be helpful in solving the question so I'm going to put all the parts down..)

a.) If z = prove that

b.) Use the binomial theorem to expand and simplify your result.

c.)By using a and b above, show that

d.) Hence show the exact value of is

e.) Show that if z = then and hence that

I know how to solve parts a to e, I'm just stuck at the very last part f.) which question is at the start of this post, please help me, thank you so so so much!