Use the fact that
Let j be the imaginary unit.
By the Product Rule for Exponents, this is equal to
Now use the trig form:
In this case, a = 4 and c = -1.
Since cosine is EVEN and sine is ODD, we have...
Don't forget to multiply by 1024 to obtain the final answer in the standard form. You should be able to easily identify the real and imaginary parts now.