# Thread: Matrix of a transform from R2 -> R2

1. ## Matrix of a transform from R2 -> R2

I honestly have been turning this problem over and over in my head for the past two days like someone chews a piece of gum after it's lost it's flavor, getting nowhere. I just can't get over the fact that a real number multiplied by a complex number is in C, not R2 anymore. Any tips?

see attached for image of problem

2. ## Re: Matrix of a transform from R2 -> R2

Hey cubejunkies.

I'm not sure where the difficulty is but if w is a real number and z is a complex number then w * z = w * (x + iy) = wx + iwy which is a complex number (generally speaking).

You have to remember that the multiplication rules for real numbers are not the same as for complex since you have the i^2 = -1 constraint.

With regards to the question, can you show us your working out for getting the mapping (i.e. the matrix)? Remember that you are sending vectors from the domain into vectors in the co-domain by some linear transformation (your matrix that you are trying to show).