We have , √3 + i
Let √3 = r cosθ …(i) and 1 = r sinθ …(ii)
Squaring and adding (i) and (ii), we get
r2(cos2θ+sin2θ) = 3 + 1 ⇒ r2 = 4 ⇒ r = 2
Substituting the value of r in (i) and (ii), we get 2 cos θ = √3 , 2 sin θ = 1
⇒ cos θ =

√3

2

, sin θ =

1

2

⇒ cos θ = cos

π

6

, isn θ = sin

π

6

Here , cos θ and sin θ both are positive.
∴ θ lies in first quadrant. ∴ θ =

π

6

∴ The required polar form is z = 2 (cos

π

6

+isin

π

6

)