If `a=cos[(4pi)/3]+i sin[(4 pi)/3]` then `(1+a)^(3n)=`

If a=cos(4 pi)/(3)+i sin(4 pi)/(3) then the value of (1+a)^(3n) is

If a=cos((4 pi)/(3))+i sin((4 pi)/(3)), then the value ((1+a)/(2))^(3n)

If a=cos((4 pi)/(3))+i sin((4 pi)/(3)), then the value ((1+a)/(2))^(3n)

If a=cos((4pi)/3)+isin((4pi)/3) then |(1,1,1),(1,a,a^2),(1,a^2,a)|

If a=cos""(4pi)/(3)+isin""(4pi)/(3) , then the value of ((1+a)/(2))^(3n) is :

z=(1-i)/(cos(pi/3)+i sin(pi/3))

If z_(1)=sqrt(2)((cos pi)/(4)+i sin((pi)/(4))) and z_(2)=sqrt(3)((cos pi)/(3)+i sin((pi)/(3))) then |z_(1)z_(2)|=

Two of the three value of (-1)^((1)/(3)) are cos((pi)/(3))+i sin((pi)/(3)) and cos((5 pi)/(3))+i sin((5 pi)/(3)) the third value is

If x_(n)=cos((pi)/(4^(n)))+i sin((pi)/(4^(n))), then x_(1)*x_(2),x_(3)...............oo

Circumcentre of DeltaABC (h,k) ,where co-ordinates of A=(2+cos(pi/3),3+sin(pi/3)) , B=(2+cos pi,3+sin pi) and C=(2+cos(4 pi/3),3+sin(4 pi/3)) , then the value of h^(2)+k^(2)=