If n ∈ N, then find the value of i n + i n + 1 + i n + 2 + i n + 3 .

Question

Philoid · Accepted Answer

As we know that,

i = √(-1 ), i² = -1, i³ = -i, i⁴ = 1

z = iⁿ + iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³

= iⁿ (1+i¹+i²+i³ )

= iⁿ (1+i-1-i)

= iⁿ(0)

= 0