Addition of complex numbers

When z1 = a1+ib1 and z2 = a2+ib2 the addition of the two z1 + z2 is defined as the complex number (a1+a2) + i(b1+b2)

Re(z1+z2) = Re(z1) + Re(z2)

Im(z1+z2) = Im(z1)+Im(z2)