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If $z = {(\frac{1}{\sqrt{3}} + \frac{1}{2} i)}^{7} + {(\frac{1}{\sqrt{3}} - \frac{1}{2} i)}^{7}$ then

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Re (z)=0

Im⁡(z)=0

Re⁡(z)>0,Im⁡(z)<0

Re⁡(z)<0,Im⁡(z)>0

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detailed solution

Correct option is B

z¯=13−12i7+13+12i7=z⇒z is purely real∴ Im⁡(z)=0

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If z=13+12i7+13−12i7then

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If $z = {(\frac{1}{\sqrt{3}} + \frac{1}{2} i)}^{7} + {(\frac{1}{\sqrt{3}} - \frac{1}{2} i)}^{7}$ then