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If z=((sqrt(3))/2+i/2)^5+((sqrt(3))/2-i/...

If `z=((sqrt(3))/2+i/2)^5+((sqrt(3))/2-i/2)^5` , then prove that `I m(z)=0.`

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`z=((sqrt(3))/(2)+(i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5)`
`z=(e^((i pi)/(6)))^(5)+(e^((-ipi)/(6)))^(5)=e^(i5pi//6)+e^(-i5pi//6)=-2"cos"(pi)/(6)=-sqrt(3)`
`R(z)=-sqrt(3)" " I(z)=0`
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