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

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

Show that ((sqrt(3))/(2) + (i)/(2))^(5) + ((sqrt(3))/(2) - (i)/(2))^(5) = -sqrt(3)

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

Prove that (sqrt(3)/(2) +(i)/(2))^(5) + (sqrt(3)/(2) -(i)/(2))^(5) is purely real.

((-1+i sqrt(3))/(2))^(6)+((-1-i sqrt(3))/(2))^(6)+((-1+i sqrt(3))/(2))^(5)+((-1-i sqrt(3))/(2))^(6)

Find the values of the following : ( sqrt3/2 + i/2)^(5) - ( sqrt3/2 - i/2)^(5)

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