What is the value of i^97?

To find the value of i⁹⁷, we first need to understand the behavior of the imaginary unit, i, which is defined as the square root of -1. The powers of i follow a cyclical pattern:

• i¹ = i
• i² = -1
• i³ = -i
• i⁴ = 1

After i⁴, the pattern repeats:

• i⁵ = i
• i⁶ = -1
• i⁷ = -i
• i⁸ = 1

This cycle continues every four powers: i, -1, -i, 1. To determine the value of i⁹⁷, we need to find the remainder of 97 when divided by 4:

97 ÷ 4 = 24 remainder 1

This tells us that i⁹⁷ corresponds to i¹ in our cycle. Therefore:

i⁹⁷ = i