Rudin makes the following statement in his Real and Complex Analysis, page 3: If z = x + iy, x and y are real, then ez = exeiy. Hence |ez| = ex. I don't understand what's happening here. If I draw ez on coordinate axes with imaginary numbers on the y-axis and real numbers on the x-axis, I get |ez| = √((ex)2 + (eiy)2. Does this equal ex somehow?