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 I m(z)=0.

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 a. R e(z)=0 b. I m(z)=0 c. R e(z)>0 d. R e(z)>0,I m(z)<0

If z=[(sqrt(3)/2)+i/2]^5+[((sqrt(3))/2)-i/2]^5 , then a. R e(z)=0 b. I m(z)=0 c. R e(z)>0 d. R e(z)>0,I m(z)<0

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

If z=((sqrt3)/(2)+(1)/(2)i)^5+((sqrt3)/(2)-(i)/(2))^5 , then (a) im(z)=0 (b) Re(z)gt0 , Im(z)gt0 (c) Re(z)gt0 , Im(z)lt0 (d) Re(z)=3

If z(2-2 sqrt(3) i)^(2)=i(sqrt(3)+i)^(4) then arg z=

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