Question

i² + i³ + ... + i⁴⁰⁰⁰ =

Options

• 1

• 0

• i

• −i

Answer 1

−i

Explanation:

∵ in = iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³ = 0, ∀ n ∈

Integer

So, i² + i³ + i⁴ + ... + i⁴⁰⁰⁰ = i − i + i² + i³ + ... + i⁴⁰⁰⁰

= −i + [i + i² + i³ + ... + i⁴⁰⁰⁰] = −i