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

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

Evaluate the following: (i) (2 + sqrt(5) )^(5) + (2 - sqrt(5) )^(5) (ii) ( sqrt(3) + 1)^(5) - ( sqrt(3) - 1)^(5) Hence, show in (ii), without using tables, that the value of ( sqrt(3) + 1)^(5) lies between 152 and 153.

Show that (sqrt3/2 + i/2)^3 = i

Express the following in the form a+bi (sqrt3 + 5i) (sqrt3 -5i)^(2) + (-4+ 5i)^(2)

If z= ((sqrt3)/(2) + (i)/(2))^(107) + ((sqrt3)/(2)-(i)/(2))^(107) , then show 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

show that ((sqrt(3)+i)/2)^6+((i-sqrt(3))/2)^6=-2

Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(3)-i)/2 d. (-sqrt(3)+i)/2