I have to solve this equation using Fourier transformation:

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.
Thank you.