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

If z=((sqrt(3))/(2)+(i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5), then prove that Im(z)=0

If z=((sqrt(3))/(2)+(i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5), then prove that Im(z)=0

(sqrt3/2+i/2)^5 - (sqrt3/2-i/2)^5=

If z=((sqrt(5))/(2)+(i)/(2))^(5)+((sqrt(5))/(2)-(i)/(2))^(5) , the prove that Im(z)=0 .

If z=((sqrt(3))/(2)+(1)/(2)i)^(5)+((sqrt(3))/(2)-(i)/(2))^(5), then (a) im(z)=0 (b) Re(z)>0,Im(z)>0(c)Re(z)>0,Im(z)<0 (d) Re(z)=3

If z=[((sqrt(3))/(2))+(i)/(2)]^(5)+[((sqrt(3))/(2))-(i)/(2)]^(5) then Re(z)=0 b.Im(z)=0 c.Re(z)>0 d.Re(z)>0,Im(z)<0

If z=((sqrt3)/(2)+(i)/(2))^(107)+((sqrt3)/(2)-(i)/(2))^(107), then what is the imaginary pary of z equal to?

If z=(sqrt(3)+i)/(2) the (iz)^(59)=