Convert the complex number in polar form: (-16)/(1+i√3)

Given expression:

(-16 / (1 + i√3)) = (-16 / (1 + i√3)) × ((1 - i√3) / (1 - i√3))

= (-16(1 - i√3)) / ((1 + i√3)(1 - i√3)) = (-16(1 - i√3)) / (1 + 3) = -4 + 4√3i

Let -4 = r cosθ and 4√3 = r sinθ.

On squaring and adding:

16 + 48 = r²(cos²θ + sin²θ)

⇒ r² = 64 ⇒ r = 8

Hence, cosθ = -1/2 and sinθ = √3/2

⇒ θ = π - π/3 = 2π/3

Thus, the required polar form is: 8(cos(2π/3) + i sin(2π/3))