Symbol Z*. The quantity given by Z* = x − iy, when the complex number Z is given by Z = x + iy. The polar form of Z* is rcosθ − irsinθ. In the Argand diagram the complex conjugate of a complex number is a reflection of the complex number about the real axis. The sum and product of Z and Z* satisfy Z + Z* = 2x, ZZ* = x2 + y2.