If `((1+i)/(1-i))^(m/2)=((1+i)/(-1+i))^(n/3)=1`. Find the G.C.D. of m,n

If ((1+i)/(1-i))^((m)/(2))=((1+i)/(1-i))^((n)/(3))=1, (m, ninN) then the greatest common divisor of the least values of m and n is .............

If i^(2)=-1 and ((1+i)/(sqrt2))^(n)=((1-i)/(sqrt2))^(m)=1, AA n, m in N , then the minimum value of n+m is equal to

If I(m,n)=int_(0)^(1)t^(m)(1+t)^(n).dt, then the expression for I(m,n) in terms of I(m+1,n-1) is:

If Sigma_( i = 1)^( 2n) sin^(-1) x_(i) = n pi , then find the value of Sigma_( i = 1)^( 2n) x_(i) .

If Sigma_( i = 1)^( 2n) sin^(-1) x_(i) = n pi , then find the value of Sigma_( i = 1)^( 2n) x_(i) .

If sum_(i=1)^(2n)sin^(-1)x_(i)=n pi then find the value of sum_(i=1)^(2n)x_(i)

If n_1, n_2 are positive integers, then (1 + i)^(n_1) + ( 1 + i^3)^(n_1) + (1 + i^5)^(n_2) + (1 + i^7)^(n_2) is real if and only if :

If n_1, n_2 are positive integers, then (1 + i)^(n_1) + ( 1 + i^3)^(n_1) + (1 + i_5)^(n_2) + (1 + i^7)^(n_2) is real if and only if :

If n_(1),n_(2) are positive integers,then (1+i)^(n_(1))+(1+i^(3))^(n_(1))+(1+i_(5))^(n_(2))+(1+i^(7))^(n_(2)) is real if and only if :

If n_1, n_2 are positive integers, then (1 + i)^(n_1) + ( 1 + i^3)^(n_1) + (1 + i_5)^(n_2) + (1 + i^7)^(n_2) is real if and only if :