I think you mean the complex number
-9 - 9√3 i
This number has modulus
|-9 - 9√3 i| = √((-9)² + (-9√3)²) = √324 = 18
and argument θ such that
tan(θ) = (-9√3) / (-9) = √3
Since -9 - 9√3 i falls in the third quadrant of the complex plane, we expect θ to be between -π and -π/2 radians, so that
θ = arctan(√3) - π = π/3 - π = -2π/3
Then the polar form is
18 (cos(-2π/3) + i sin(-2π/3))
and -2π/3 is the same angle as 2π - 2π/3 = 4π/3, so the correct choice is
18 (cos(4π/3) + i sin(4π/3))
