Solution
= Solution
Using <Euler's formula>, the difference of the two <complex exponentials> is $2i\sin(\pi/4)=i\sqrt2$. Hence
$$
(i\sqrt2)^4=4i^4=4,
\qquad\boxed{\operatorname{Re}=4,\qquad\operatorname{Im}=0.}
$$
These are the <real part> and <imaginary part>, respectively.