eigenvector, complex roots

I am asked to solve the system:

dx/dt =

-2 -2

4 2

with the initial condition

x(0) =

-1

-1

I find the roots of the characteristic equation to be +/- 2i

and the associated eigenvector to be

1

2-2i

from euler's formula, i find that x(t) = [cos(2t)+isin(2t)](1 : 2-2i)

x(t) =

cos2t + isin2t

2cos2t-2icos2t+2isin2t+2sin2t

x(t) =

cos2t

2cos2t + 2sin2t

+

(i)

sin2t

-2cos2t+2sin2t

with the initial condition, i find c1 = -3 and c2 = -5/2.

Where am I wrong (submitted answer is not correct)

Thanks, let me know if anything needs more explanatioin.