I was asked to find a basis beta for V such that [T]_beta is a diagonal matrix. V=C^2 and T is defined by T(z,w) = (z+iw, iz+w) for C = complex. I don't quite understand the expression C^2, I know C can be represented by a plane with the real and imaginery axis, but how abt C^2? and also, how do i figure out the basis for this? I used (1,0) and (0,1) as my basis and I got the right answer.. but the basis doesn't seem right to me intuitively.