The hermitian form

Hc(x) = c*x1t*x1 + 2*x2t*x2 - i*x1t*x2 + i*x2t*x1 + x1t*x3 + x3t*x1

+i*x2t*x3 - i*x3t*x2 (sorry, it`s a bit messy)

For which value of c is Hc ositive definite?

I have tried to find the eignvalue in terms of c by trying to solve the

charactiristic polynomial, but seems too complicate to do, I`ve also tried

to solve by completing the square but not so successful.

So is there any way to solve this without using computer softwares like

maple? Thanks