Let z be a complex number such that Z = 2 then maximum possible value of z+2z is

Let z=2(cos⁡θ+isin⁡θ).Nowz+2z=2(cos⁡θ+isin⁡θ)+(cos⁡θ−isin⁡θ)=3cos⁡θ+isin⁡θ⇒z+2z2=9cos2⁡θ+sin2⁡θ=1+4(1+cos⁡2θ)≤9∴ maximum possible value of z+2z is 3 whichis attained when z = 1