Show that there is no positive integer, n for which `sqrt(n-1) + sqrt(n+1) ` is rational .

The least positive integer n for which (sqrt(3)+i)^(n)=(sqrt(3)-i)^(n) is

The smallest positive integer n for which (1+i sqrt(3))^(n / 2) is real is

The smallest positive integer n for which (1+i)^(n) is purely imaginary is

The smallest positive integer for which (1 + i)^(2n)=(1 -l)^(2n) is

The least positive integer n, for which ((1+i)^(n))/((1-i)^(n-2)) is positive is

Prove that 2^(n) gt n for all positive integers n.

If n is a positive integer, then: (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is:

Find the least positive integral value of n, for which ((1-i)/(1+i))^n , where i=sqrt(-1), is purely imaginary with positive imaginary part.

If n is a positive integer, then (1+i)^(n)+(1-i)^(n)=

For any positive integer n, prove that (n^(3) - n) is divisible by 6.