" (c) "((1+i)^(n))/((1-i)^(n-2))

The least positive integer n such that ((2i)^n)/((1-i)^(n-2)),i=sqrt(-1) , is a positive integer,is ______

The complex number (2^(n))/((1+i)^(2n))+((1+i)^(2n))/(2^(n)),n varepsilon I is equal to

Find the integral values of n for the equations : (a) (1+i)^(n)=(1-i)^(n) (b) (1-i)^(n)=2^(n)

" *.i).i) If "n" is an integer then show that "(1+i)^(2n)+(1-i)^(2n)=2^(n+1)cos(n pi)/(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

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 (1+i)^(2n)+(1-i)^(2n)=-2^(n+1)(where,i=sqrt(-1) for all those n, which are

If (1+i)^(2n)+(1-i)^(2n)=-2^(n+1)(where,i=sqrt(-1) for all those n, which are