Evaluate.
(i) `i^(1998)`
(ii)` i^(-9999)`
(iii) `(-sqrt-1)^(4n-3)`,n `ne` N

Find the value of 1+i^(2)+i^(4)+i^(6)+...+i^(2n), where i=sqrt(-1) and n in N.

int (a+sqrt x)^n /sqrtxdx, n ne -1

If A^(n) = 0 , then evaluate (i) I+A+A^(2)+A^(3)+…+A^(n-1) (ii) I-A + A^(2) - A^(3) +... + (-1) A^(n-1) for odd 'n' where I is the identity matrix having the same order of A.

The value of sum_(n=0)^(100)i^(n!) equals (where i=sqrt(-1))

For an positive integer n, prove that : i^(n) + i^(n+1) + i^(n+2) + i^(n+3) + i^(n+4) + i^(n + 5) + i^(n+6) + i^(n+7) = 0 .

Assign the position of the elements having outer eletronic configuration i) ns^(2)np^(4) for n=3 ii) (n-1)d^(2)ns^(2) for n=4 iii) (n-2)f(n-1)d^(1)ns^(2) for n=6, in the periodic table.

The value of sum sum_(n=1)^(13)(i^n+i^(n+1)) ,where i=sqrt(-1) equals

If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following holds for all nge1 by the principle of mathematica induction? (A) A^n=2^(n-1) A+(n-1)I (B) A^n=nA+(n-1) I (C) A^n=2^(n-1) A-(n-1)I (D) A^n=nA-(n-1) AI

For positive integers n_1,n_2 , the value of the expression : (1+i)^(n_1)+(1+i^3)^(n_1) +(1+i^5)^(n_2)+ (1+i^7)^(n_2) , where i= sqrt(-1) is a real number if and only if :