I have to solve this equation using Fourier transformation:

$\displaystyle u_{tt}-c^2 u_{xx}+u_{t} - a u_{x}=0$

$\displaystyle u(x,0)=f(x)$

$\displaystyle u_{t}(x,0)=g(x)$

I have problem with finding the square root $\displaystyle \sqrt{1/4 - k^2c^2 + iak}$, which appears in solution.

Thank you.