Solution
= Solution
The <complex sine> identity is
$$
\sin(x+iy)=\sin x\cosh y+i\cos x\sinh y.
$$
It follows either from the exponential definition of <sine> or its addition formula, using $\sin(iy)=i\sinh y$ and $\cos(iy)=\cosh y$. Consequently
$$
\boxed{\operatorname{Re}\sin(2+3i)=\sin2\cosh3,\qquad \operatorname{Im}\sin(2+3i)=\cos2\sinh3.}
$$
The angles $2$ and $3$ in these functions are dimensionless; the real trigonometric argument is measured in radians.