Prove that `4+5(-1/2+(isqrt3)/2)^(334)+3(-1/2+(isqrt3)/2)^(335)=isqrt3`

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

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+isqrt3)/(2))^(3n)+((-1-isqrt3)/(2))^(3n)

If i=sqrt-1, then 4+5(-1/2+(isqrt3)/2)^334+3(-1/2+(isqrt3)/2)^365 is equal to (1) 1-isqrt3 (2) -1+isqrt3 (3) isqrt3 (4) -isqrt3

If i=sqrt(-1) then 4+5(-1/2+(isqrt3)/2)^334+3(-1/2+(isqrt3)/2)^365 is equal to

((-1+isqrt3)/(2))^(6)+((-1-isqrt3)/(2))^(6)

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

Prove that ((-1 + isqrt3)/(2))^(n) + ((-1-isqrt3)/(2))^(n) is equal to 2 if n be a multiple of 3 and is equal to -1 if n be any other integer

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