# Real and Imaginary matrix

I have a 2 by 2 matrix T: {{x, y}, {-y, x}} where x is the real part of some complex number and y is the imaginary part of something complex number. Let's say z1 = 1 + i2. How would I do T[z1] where x would be 1 and y would be 2?

• Try {#, Cross[#]} &@ReIm[1 + 2 I] or {IdentityMatrix[2], -LeviCivitaTensor[2]}.ReIm[1 + 2 I] and report back. – J. M. will be back soon Apr 12 '16 at 17:15
• T[z_] = {{Re[z], Im[z]}, {-Im[z], Re[z]}}; z1 = 1 + 2 I; T[z1] evaluates to {{1, 2}, {-2, 1}} – Bob Hanlon Apr 12 '16 at 19:17

r = IdentityMatrix[2];

Note i.i yields {{-1,0},{0,-1}}= -IdentityMatrix[2].