For any integer n, the argument of `((sqrt3+i)^(4n+1))/((1-isqrt3)^(4n))`

The argument of (1-isqrt(3))/(1+isqrt(3)) , is

The principal argument of (1-isqrt(3))/(1+isqrt(3))

If n is any integer, then the value of (-sqrt(-1))^(4n+3)

For any positive n, let f(n)=(4n+sqrt(4n^(2)-1))/(sqrt(2n+1)+sqrt(2n-1)) . Then ((Sigma_(k=1)^(40)f(k))/(100)) is equal to

If n is any positive integer, write the value of (i^(4n+1)-i^(4n-1))/2 .

Write the argument of (1+isqrt(3))(1+i)(costheta+isintheta) .

For positive integer n_1,n_2 the value of the expression (1+i)^(n1) +(1+i^3)^(n1) (1+i^5)^(n2) (1+i^7)^(n_20), where i=sqrt-1, is a real number if and only if (a) n_1=n_2+1 (b) n_1=n_2-1 (c) n_1=n_2 (d) n_1 > 0, n_2 > 0

If n is a positive integer, then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is (1) an irrational number (2) an odd positive integer (3) an even positive integer (4) a rational number other than positive integers

If rArr I_(n)=int_(0)^(pi//4) tan ^(n)x dx , then for any positive integer, n, the value of n(I_(n+1)+I_(n-1)) is,

For and odd integer n ge 1, n^(3) - (n - 1)^(3) + …… + (- 1)^(n-1) 1^(3)