Math doubt

any way of doing this without putting x+iy expanding and then differentiating?

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is the answer B ?

as per key it is d

Put z=e^itheta expand it you will get mod =2root(2-cĀ²theta-4 costheta+4cosĀ³theta) and for max value costheta=-1/2 you will get root 13 as ansā€¦

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