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If $x + i y = \frac{3}{\cos θ + i \sin θ + 2}$ than $4 x - x^{2} - y^{2}$

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Correct option is B

1x+iy=cos⁡θ+23+isin⁡θ3⇒x−iyx2+y2=cos⁡θ+23+isin⁡θ3⇒xx2+y2=cos⁡θ+23Also x2+y2=9(2+cos⁡θ)2+sin2⁡θ=95+4cos⁡θ∴4x−x2+y2=4(cos⁡θ+2)3−1x3+y3=4cos⁡θ+53⋅95+4cos⁡θ=3

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If x+iy=3cos⁡θ+isin⁡θ+2 than 4x−x2−y2

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If $x + i y = \frac{3}{\cos θ + i \sin θ + 2}$ than $4 x - x^{2} - y^{2}$