Hey, iv been stuck on this question for a few hours now and was wondering if anyone could give me some help.

Determine the general solution of the system:

x'= x-y y'= 2x+3y

its to be in complex form and im to then find the solution satisfying x(0)=0, y(0)=2 in real form

iv managed to get as far as finding the eigenvalues which i got to be 2+i and 2-i but iv not been able to calculate the eigenvectors. Any help you can give me would be great.

thanks Caitlin