Simplify Complex Number Fraction

[FelixISF]

1. The problem statement, all variables and given/known data

\frac{(cos60 - isin60)^5 * (cos45 - isin45)^3}{(cos15-isin15)^7}


2. Relevant equations



3. The attempt at a solution

I have had several tries so far, but simply do not know what to do. Would somebody be so kind and simplify this expression step by step. I couldn't find any solved problems like this on the internet and am lost!


Thanks!

[Matthollyw00d]

Use
e-ix=cosx - isinx
to simplify everything into base e, then use laws of exponents, and you should be able to come to an answer.

[FelixISF]

Thanks!