[" (1) "2t+6t+3t=0],[" (iii) "i^(n)+i^(n+1)+i^(n+2)+i^(n+3)]

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

If i= sqrt-1 and n is a positive integer , then i^(n) + i^(n + 1) + i^(n + 2) + i^(n + 3) is equal to

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) (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 .

The simplified form i^n+i^(n+1)+i^(n+2)+i^(n+3) is

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

(I n (3)) (I n) = (I n (2)) ^ (2)

The simplified form of i^(n)+i^(n+1)+i^(n+2)+i^(n+3) is