Solution
= Solution
Use the complex <sine> identity $\sin(x+iy)=\sin x\cosh y+i\cos x\sinh y$, then multiply by $x+iy$. The <real part> and <imaginary part> are
$$
\boxed{x\sin x\cosh y-y\cos x\sinh y,\qquad x\cos x\sinh y+y\sin x\cosh y.}
$$
= Solution
Use the complex <sine> identity $\sin(x+iy)=\sin x\cosh y+i\cos x\sinh y$, then multiply by $x+iy$. The <real part> and <imaginary part> are
$$
\boxed{x\sin x\cosh y-y\cos x\sinh y,\qquad x\cos x\sinh y+y\sin x\cosh y.}
$$