Question

How do you simplify `{(cos pi/15 + isin pi/15)^10 + (cos pi/15 - isin pi/15)^10 } /(cos pi/3 + i sin pi/3)^6`?

Answer 1

`-1`

Explanation:

For brevity, use `cis a =e^(ia)=cos a + i sin a`

Then, `(cis a)^n=cis na`.

Now, the given expression is condensed to

`(cis((2pi)/3)+cis((-(2pi)/3) )) /(cis (2pi)`

`=(2 cos ((2pi)/3))/(1)`

`=2cos (pi-pi/3)=-2 cos(pi/3)=-2(1/2)=-1`