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

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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.