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

For a positive integer n, what is the value of i^(4n+1) ?

For any positive integer n, find the value of i^(n)+i^(n+1)+i^(n+2)+i^(n+3)+i^(n+4)+i^(n+5)+i^(n+6)+i^(n+7) .

Find the value of : (1+i)^n, n inN

If n is any positive integer,write the value of (i^(4n+1)-i^(4n-1))/(2)

For positive integer n_1,n_2 the value of the expression (1+i)^(n1) +(1+i^3)^(n1) (1+i^5)^(n2) (1+i^7)^(n_20), where i=sqrt-1, is a real number if and only if (a) n_1=n_2+1 (b) n_1=n_2-1 (c) n_1=n_2 (d) n_1 > 0, n_2 > 0

If rArr I_(n)=int_(0)^(pi//4) tan ^(n)x dx , then for any positive integer, n, the vlau of (I_(n+1)-I_(-1)) is,

If (sqrt(3)+i)^(n)=x_(n)+iy_(n) and n is a positive integer then the value of x_(n-1)y_(n)-x_(n)y_(n-1)=

If n be a positive integer, then prove that (1+i)^n+(1-i)^n=2^(n/2+1)."cos"((npi)/4)

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