= ⇒ z − = Multiplying the numerator and denominator by the conjugate of the denominator, we get z − = ⇒ z − = − i Example . Show that (i) is real and (ii) is purely imaginary. (i) Let z = . Then, we get z = = ( z = z = z = z ⇒ is real.
(ii) Let z = Here, i = = = + i . ( ) and i = = = - i . ( ) - - Complex Numbers Now z = ⇒ z = (by ( ) and ( )) Then by definition, z = = (using properties of conjugates) = ⇒ z = − z . Therefore, z = is purely imaginary.