The correct option is C.
polar representation: z = x + i y = r (cosθ + i sinθ)
where, r is the modulus=|z| and θ = argument of the complex number
taking the modulus, |z| as from polar representation
[tex]|2\sqrt{3} +3i| =\sqrt{(2\sqrt{3})^{2}+2^2 } = \sqrt{12+4}=\sqrt{16} =4=r[/tex]
taking argument,
[tex]cos(arg(2\sqrt{3}+2i ))=\frac{x}{|z|} =\frac{2\sqrt{3}}{4} =\frac{\sqrt{3}}{2}[/tex]
[tex]arg(2\sqrt{3} +2i)\\[/tex] = π/6= θ
therefore, polar representation: 4(cos(π/6)+ i sin(π/6))
The correct option is C.
learn more about polar representation of complex number here:
https://brainly.com/question/27680000
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