Solution
= Solution
The <complex sine function> obeys
$$
\sin(x+iy)=\sin x\cosh y+i\cos x\sinh y.
$$
Thus
$$
\boxed{\operatorname{Re}(\sin z)=\sin x\cosh y,
\qquad \operatorname{Im}(\sin z)=\cos x\sinh y}.
$$
= Solution
The <complex sine function> obeys
$$
\sin(x+iy)=\sin x\cosh y+i\cos x\sinh y.
$$
Thus
$$
\boxed{\operatorname{Re}(\sin z)=\sin x\cosh y,
\qquad \operatorname{Im}(\sin z)=\cos x\sinh y}.
$$