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If $3^{49} (x + i y) = {(\frac{3}{2} + \frac{i}{2} \sqrt{3})}^{100}, y \in N$ and $x = k y,$ then value of $k$ is

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Correct option is B

We have 349|x+iy|=|3/2+3i/2|100⇒349x2+y2=(9/4+3/4)50⇒x2+y2=3⇒(y)1+k2=3⇒1+k2=3,3/2,1, as y∈N⇒k=±22,±5/2,0Out of the given values, we have k=±22.

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If 349(x+iy)=32+i23100,y∈N and x=ky, then value of k is

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If $3^{49} (x + i y) = {(\frac{3}{2} + \frac{i}{2} \sqrt{3})}^{100}, y \in N$ and $x = k y,$ then value of $k$ is