Question 882013
I don't really understand the e to the power -pi/6 -pi/4 part, so, I solve in standard form(without e to the power).
All that you have solved is correct. I think the problem is in the division part. 
After putting the values, we get 2*((cos pi/6)-(sin pi/6)i)/(2^(3/2)((cos pi/4)+(sin pi/4)i))
where -cos pi/6=cos pi/6
multiply and divide by (cos pi/4)-(sin pi/4)i)
=> ((cos pi/6 - sin pi/4i)*(cos pi/4 - sin pi/4i))/(sqrt2(cos pi/4 + sinpi/4i)*(cos pi/4 - sin pi/4i)) 
=>((cos pi/6)*(cos pi/4)-(sin pi/6)*(cos  pi/4)i-(cos pi/6)*(sin pi/4)i-(sin pi/6)*(sin pi/4))/(sqrt 2)
Using cos(x+y)=cosx*cosy-siny*cosx
and sin(x+y)=sinx*cosy-siny*cosx
=>(2^(-1/2))*(cos(pi/6 + pi/4)-sin(pi/6 + pi/4)i)
I hope this helps.