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
a2 + 4 = a2 , which is not possible .
Hence (D) is the correct answer.