Solution
= Solution
Powers of the <imaginary unit> repeat in blocks $i,-1,-i,1$, each with sum zero. The first $44$ terms comprise eleven complete blocks; the last is $i^{45}=i$. Applying <Euler's formula> to the resulting <complex exponential> gives $e^i=\cos1+i\sin1$. Hence
$$
\boxed{\Re z=\cos1,\qquad\Im z=\sin1.}
$$
The <angles> here are in <radians>.