[4+5((-1)/(2)+(i sqrt(3))/(2))^(334)+3((-1)/(2)+(i sqrt(3))/(2))^(365)=],[(1)1-i sqrt(3)quad " 3) "i sqrt(3)quad " 4) "-i sqrt(3)]

4+5(-(1)/(2)+(isqrt3)/(2))^(334)+3(-(1)/(2)+(isqrt3)/(2))^(365)

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

4 + 5 ( - (1)/(2) + (isqrt3)/(2))^(334) + 3 ( - (1)/(2) + (isqrt3)/(2))^(365) =

((-1+i sqrt(3))/(2))^(3 n)+((-1-i sqrt(3))/(2))^(3 n)=

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)

If isqrt(-1) , then 4+5(-(1)/(2)+(isqrt(3))/(2))^(334)+3(-(1)/(2)+(isqrt(3))/(2))^(365) is

If i=sqrt(-1) , then 4+5(-1/2+(isqrt(3))/2)^(334)+3(-1/2+(isqrt(3))/2)^(365) is equal to : a) 1-isqrt(3) b) -1+isqrt(3) c) isqrt(3) d) -isqrt(3)

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

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

the value of ((-1+sqrt(3)i)/(2))^(3n)+((-1-sqrt(3)i)/(2))^(3n)=