Solution
= Solution
Expand the defining <complex exponential functions>:
$$
\cosh(x+iy)=\frac{e^{x+iy}+e^{-x-iy}}2
=\cosh x\cos y+i\sinh x\sin y.
$$
Thus the <real part> and <imaginary part> of the <hyperbolic cosine> are
$$
\boxed{\operatorname{Re}\cosh z=\cosh x\cos y,\qquad
\operatorname{Im}\cosh z=\sinh x\sin y.}
$$