Consider the real function of two real variables given by $$u(x, y)=e^{2x}[\sin 3x\cos 2y\cosh 3y-\cos 3x\sin 2y\sinh 3y].$$ Let $v(x, y)$ be the harmonic conjugate of $u(x, y)$ such that $v(0, 0) = 2$. Let $z = x+iy$ and $f(z) = u(x, y) + iv(x, y)$, then find the value of $4 + 2if (i\pi)$.
I know that $v(x, y)$ can be calculated by solving the Cauchy-Riemann equations. Is there any short method for this problem apart from above?