Find the least positive integer n such that `((1+i)/(1-i))^(n)=1`.

The least positive integer n such that ((2i)/(1 + i))^(n) is a positive integer is

Find the least positive integer n such that 1 + 6 + 6^(2) + …. + 6^(n) gt 5000 .

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

Find the least positive integer n such that 1 + 6 +6^2 + … + 6^n gt 5000

If ((1+i)/(1-i))^(m)=1 , then find the least positive integral value of m.

Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2 + (1 +x)^3 + (1 + x)^4 +........+ (1+x)^49 + (1 + mx)^50 is (3n + 1) .^51C_3 for some positive integer n. Then the value of n is

If x and y are positive real numbers and m, n are any positive integers, then Prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt =1/4