The reciprocal of complex numbers is helpful in the process of dividing one complex number with another complex number. The process of division of complex numbers is equal to the product of one complex number with the reciprocal of another complex number.. The reciprocal of the complex number z = a + ib is z−1=1a+ib=a−iba2+b2=aa2+b2+i(−b)a2+b2z−1=1a+ib=a−iba2+b2=aa2+b2+i(−b)a2+b2. This also shows that z≠z−1z≠z−1.