Writing complex number in standard form

Question

I am trying to do a question which asks me to express

$z=$ $\frac{2+7i}{i(-2+2i)^{99}}$ in standard form.

Can anyone tell me how to use DeMoivre’s Theorem to get the answer?

Answer 1

$(i-1)^4=-4.$ Hence $(i-1)^{99}= ((i-1)^4)^{24}(i-1)^3=4^{24}(i-1)^3.$

Can you proceed ?