`((sqrt(3))/(2)+(i)/(2))^(5)-((sqrt(3))/(2)-(i)/(2))^(5)=?`

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

For the system of equations given by x^(5)+y^(5)=33 and x+y=3, the possible ordered pair(s) of (x,y) can be (A) ((3)/(2)+(sqrt(17))/(2)i,(3)/(2)-(sqrt(17))/(2)i)(B)(3)/(2)+(sqrt(19))/(2)i,(3)/(2)-(sqrt(19))/(2)i)(C)(3)/(2)+(sqrt(19))/(2)i,(3)/(2)-(sqrt(19))/(2)i)(D)(3)/(2)-(sqrt(19))/(2)i,(3)/(2)+(sqrt(19))/(2)i])

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

Prove that 4+5(-(1)/(2)+(i sqrt(3))/(2))^(334)+3(-(1)/(2)+(i sqrt(3))/(2))^(335)=i sqrt(3)

If i=sqrt(-1), then 4+5(-(1)/(2)+i(sqrt(3))/(2))^(334)+3(-(1)/(2)+i(sqrt(3))/(2))^(335) is equal to-

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)

If i=sqrt(-)1, then 4+5(-(1)/(2)+(i sqrt(3))/(2))^(334)+3(-(1)/(2)+(i sqrt(3))/(2))^(365) is equal to (1)1-i sqrt(3)(2)-1+i sqrt(3)(3)i sqrt(3)(4)-i sqrt(3)

Find the principal argument of the complex (1+i)^(5)(1+sqrt(3i))^(2) number ((1+i)^(5)(1+sqrt(3i))^(2))/(-2i(-sqrt(3)+i))