# solving pde

$u_{tt}-c^2 u_{xx}+u_{t} - a u_{x}=0$
$u(x,0)=f(x)$
$u_{t}(x,0)=g(x)$
I have problem with finding the square root $\sqrt{1/4 - k^2c^2 + iak}$, which appears in solution.