Is this correct anyone;

C is the group of all complex numbers under addition

O : C ----> C

z ----> z + iz

For all z1,z2 E C

O (z1+z2) = z1 + z2 + iz1 + iz2 = z1+iz1 + z2+iz2 = O (z1) + O (z2)

Hence O satisfies the homomorphism property and so is a homomorphism.