What is the result of i raised to the power of 4 (i⁴)?

To find the value of ( i^4 ), we first need to understand the properties of the imaginary unit ( i ), which is defined as the square root of -1. It's important to know how powers of ( i ) repeat in a cycle.

1. ( i^1 = i )
2. ( i^2 = -1 ) (by definition of ( i ))

3. ( i^3 = i^2 \times i = -1 \times i = -i )
4. ( i^4 = i^2 \times i^2 = (-1) \times (-1) = 1 )

Thus, when ( i ) is raised to the fourth power, it equals 1. This pattern shows that every time we raise ( i ) to a multiple of 4, the result will always reset back to 1, confirming that ( i^4 ) indeed equals 1.

Recognizing this repetitive pattern in powers of ( i ) helps in understanding why the result of ( i^4 ) is 1.