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

Show that ((-1+sqrt(3)i)/2)^n+((-1-sqrt(3i))/2)^n is equal to 2 when n is a multiple of 3 and is equal to -1 when n is any other positive integer.

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

[(sqrt(5)+i/2)(sqrt(5)-i2)]-:(6+i5)

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

If z= ((sqrt3)/(2) + (i)/(2))^(107) + ((sqrt3)/(2)-(i)/(2))^(107) , then show that Im(z)=0

Show that : (3sqrt(2)-2sqrt(3))/(3sqrt(2)+2sqrt(3))+(2sqrt(3))/(sqrt(3)-sqrt(2))=11

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

Show that : (1)/(3-2sqrt(2))- (1)/(2sqrt(2)-sqrt(7)) + (1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5 .

The point z_1=3+sqrt(3)i and z_2=2sqrt(3)+6i are given on a complex plane. The complex number lying on the bisector of the angel formed by the vectors z_1a n dz_2 is z=((3+2sqrt(3)))/2+(sqrt(3)+2)/2i z=5+5i z=-1-i none of these

Show that: 1/(3-sqrt(8))-1/(sqrt(8)-sqrt(7))+1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+1/(sqrt(5)-2)=5