Prove that : `(i)" "i^(n) + i^(n+1) + i^(n+2) + i^(n+3) = 0` `(ii)\ (1+i)^(4) xx (1 + (1)/(i))^(4) = 16`.

Prove that : I_(n)^(-1)=I_(n)

Prove that (1 + i)^(n) + (1 - i)^(n) = 2^((n + 2)/(2)) cos (n pi)/(4)

Prove that i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0 for all n inN

1 + i^(2n) + i^(4n) + i^(6n)

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 .

Prove that i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0 , for all n in N .

Show that : (i) {i^(19) + (1/i)^(25)}^(2) = -4 " "(ii) {i^(17) - (1/i)^(34)}^(2) = 2i (iii) {i^(18) + (1/i)^(24)}^(3) = 0 " " (iv) i^n + i^(n+1) + i^(n +2) + i^(n + 3) = 0 , for all n in N .

Evaluate (i^(4n+1) - i^(4n-1)) .

Prove that: (i) (1-i)^(2)=-2i (ii) (1+i)^(4)xx(1+(1)/(i))^(4)=16 (iii) {i^(19)+((1)/(i))^(25)}^(2)=-4 (iv) i^(4n)+i^(4n+1)+i^(4n+2)+i^(4n+3)=0 (v) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25)=1+4i .