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$If Z = \frac{\sqrt{3} + i}{2}, then {[Z^{101} + i^{103}]}^{105} is equal to$

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Correct option is C

Given, z=3+i2=i[1−i3]2=−iw Consider, z101+i103=(−iw)101+i103=−iw2−i=iw Now, z101+i103105=(iw)105=i Also z=−iwz2=(−iw)2=i2w2=−w2z3=(−iw)3=−i3⋅w3=iz101+i103=z3

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If Z=3+i2, then Z101+i103105 is equal to

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$If Z = \frac{\sqrt{3} + i}{2}, then {[Z^{101} + i^{103}]}^{105} is equal to$