Powers of i Calculator

The imaginary unit, i, is defined as the square root of -1. When raised to integer powers, it follows a repeating cycle of four values.

The Cycle:

• i¹ = i
• i² = -1
• i³ = -i
• i⁴ = 1

This cycle repeats every four powers. To find the value of iⁿ for any integer n, we can find the remainder when n is divided by 4. The value of iⁿ is the same as i raised to the power of that remainder.

For example, to find i¹¹, we calculate 11 mod 4, which is 3. Therefore, i¹¹ = i³ = -i.