Show that Re z z z2 and that Im z z z2iSolutionLet z x

Show that Re (z) = (z + z*)/2 and that Im (z) = (z - z*)/2i.

Solution

Let, z = x + iy

where x and y are real but z is a complex number.

And Re (z) = x and Im (z) = y

So, z^* = x - iy

Now (z + z^* ) / 2 = (x + iy + x - iy) / 2 = x = Re (z)

Also (z - z^* ) / 2 = [(x + iy) - (x - iy)] / 2i = Im (z)