Question

Evaluate the following: i³⁰ + i⁴⁰ + i⁵⁰ + i⁶⁰ 

Answer 1

We know that, i² = – 1, i³ = – i, i⁴ = 1
= (i⁴)⁷ i² + (i⁴)¹⁰ + (i⁴)¹² i² + (i⁴)¹⁵
= (1)⁷ (–1) + (1) + (1)¹⁰ + (1)¹² (– 1) + (1)¹⁵
= – 1 + 1 – 1 + 1
= 0.