For a positive integer n, find the value of `(1-i)^n` (1-1/i)^n`

If n is any positive integer, then the value of frac{i^(4n+1)-i^(4n-1)}{2} equals

Select the correct answer from the given alternatives. If n is an odd positive integer then the value of 1 + (i)^(2n) + (i)^(4n) + (i)^(6n) is …….. .

If n is an odd positive integer then the value of (1+ i^(2n) + i^(4n) + i^(6n) ) ?

In a triangle ABC , if (b+c) / 11 = (c+a) / 12 = (a+b) / 13 then cosA / l = cosB / m = cosC / n where l, m, n are least positive integer. Find the value of (l+m+n) .

If m, n, p, q are four consecutive integers, then the value of ( i^m + i^n + i^p + i^q ) is

For positive integer n, 10^(n-2) > 81n if .....

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

Solve the following: Find the value of ((1 + i)^(2n) - (1 - i)^(2n)) / ((1 + omega^4 - omega^2) (1 - omega^4 + omega^2))

Select and write the correct answer from the given alternatives in each of the following: The smallest positive integral value of n for which ((1 - i) / (1 + i))^n is purely imaginary with positive imaginary part is