`(1+isqrt3)^(9)=`

If n is a positive integer and (1+isqrt3)^(n)+(1-isqrt3)^(n)=2^(n+1)costheta , then the value of theta is

The least positive integer n for which ((1+i sqrt3)/(1-isqrt3))^(n)=1, is

If ((1+isqrt3)/(1-isqrt3))^(n) is an integer, then n is

The value of ((-1 + isqrt3)/(2))^(36) + ( (-1 - isqrt3)/(2))^(36) =

The value of ((-1 + isqrt3)/(2))^(100) + ((-1-isqrt3)/(2))^(100) is :

The modulus and the amplitude of (1+isqrt3)^(2) are respectively-

What is the value of (-1+isqrt3)^(48) ?

Prove that ((-1 + isqrt3)/(2))^(3) is a positive integer

The product of all the values of (1+isqrt3)^(3/4) is equal to

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