Second Order Linear Difference Equations with constant Coefficient - The Homogeneous

Hi,

I have a problem with part of this example - "Solve the difference equation $\displaystyle u_{n}=2u_{n-1}-2u_{n-2}$, subject to initial conditions $\displaystyle u_{0}=2, u_{1}=3$"

I know what the characteristic polynomial is, how to calculate its zeros, but when it comes to solving $\displaystyle c_{1}+c_{2}=2$ and $\displaystyle c_{1}(1+i)+c_{2}(1-i)=3$ I find it difficult. I understand that we can present $\displaystyle c_{1}=x+iy$ and than we can calculate $\displaystyle c_{2}$, but how do we calculate $\displaystyle x$ and $\displaystyle y$? How can I establish that $\displaystyle 1+i=\sqrt{2}(\cos(\frac{\pi}{4})+i\sin(\frac{\pi}{ 4}))$? I would be greateful if anyone could help me. Thanks in advance.