What does i raised to the power of 6 (i⁶) equal?

To determine the value of (i^6), it's important to understand the properties of the imaginary unit (i), which is defined as the square root of (-1). One useful aspect of (i) is that its powers cycle every four exponents:

• (i^1 = i)
• (i^2 = -1)

• (i^3 = -i)
• (i^4 = 1)

After (i^4), the pattern repeats, so:

• (i^5 = i) (which is (i^1))
• (i^6 = -1) (which is (i^2))

Since (i^6) is equivalent to (i^2), it equals (-1). This established cycle allows for quick computation of powers of (i) without needing to calculate each successive power individually. Thus, the correct value for (i^6) is indeed (-1).