simplify : `i^(n+100)+i^(n+50)+i^(n+48)+i^(n+46)`

Simplify the following : (i) 1+ i^(5)+i^(10)+i^(15) (ii) (1+i)^(4)+(1+(1)/(i))^(4) (iii) i^(n)+i^(n+1)+i^(n+2)+i^(n+3)

If n in N, then find the value of i^(n)+i^(n+1)+i^(n+2)+i^(n+3)

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) .

For any 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 .

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

lim_ (n rarr oo) sum_ (i = 1) ^ (n) (i ^ (3)) / (i ^ (4) + n ^ (4))

Find the value of i^(n)+i^(n+1)+i^(n+2)+i^(n+3) for all n in N.