Q: If a > 0, a ∈ R, z = a + 2i and z|z| – az + 1 = 0 then

(A) z is always a positive real number

(B) z is always a negative real number

(C) z is purely imaginary number

(D) such a complex z does not exist.

Sol. Putting z = a + 2i in the given equation and comparing imaginary parts, we get

a^{2} + 4 = a^{2} , which is not possible .

Hence (D) is the correct answer.