If z+i / 4z + zi is purely real Δz = x + iy (x, y ∈ R) then one of the possibility is

Question

If \(\frac{z+i}{4z+zi}\) is purely real Δz = x + iy (x, y ∈ R) then one of the possibility is

(1) x ≠ 0, y ≠ –1 

(2) x = 0, y = –1 

(3) x = –1, y = 1 

(4) x = 1, y ≠ –1

Answer 1

(2) x = 0, y = –1