The least positive integer n for which `((1+i)/(1-i))^n= 2/pi sin^-1 ((1+x^2)/(2x))`, where `x> 0 and i=sqrt-1` is

The least positive integer n for which ((1+i)/(1-i))^(n)=(2)/(pi)(sec^(-1)""(1)/(x)+sin^(-1)x) (where, Xne0,-1leXle1andi=sqrt(-1), is

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

The equation z^(2)-i|z-1|^(2)=0, where i=sqrt(-1), has.

Let n be a positive integer such that sin(pi/(2n))+cos(pi/(2n))=(sqrt(n))/2 Then

The value of sum_(n=0)^(50)i^(2n+n)! (where i=sqrt(-1)) is

Evaluate the following (i) sin ( pi/2 - sin^(-1) ( (-1)/2)) (ii) sin(pi/2 - sin^(-1)(- sqrt3/2))

The positive integer value of n >3 satisfying the equation 1/(sin(pi/n))=1/(sin((2pi)/n))+1/(sin((3pi)/n))i s

If, for a positive integer n, the quadratic equation, x(x + 1) + (x + 1)(x + 2) +.....+ (x +bar( n-1))(x + n) = 10n has two consecutive integral solutions, then n is equal to

if alpha and beta the roots of z+ (1)/(z) =2 (cos theta + i sin theta ) where 0 lt theta lt pi and i =sqrt(-1) show that |alpha - i |= | beta -i|

Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form : (i) {P, R, I, N, C, A, L} (a) { x : x is a positive integer and is a divisor of 18} (ii) { 0 } (b) { x : x is an integer and x^(2) – 9 = 0 } (iii) {1, 2, 3, 6, 9, 18} (c) {x : x is an integer and x + 1= 1 } (iv) {3, –3} (d) {x : x is a letter of the word PRINCIPAL}