What is the value of i to the power of 4?

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The mathematical expression i to the power of 4, which is written as i4, is equal to 1. To understand why, we first need to recall what i represents. In mathematics, i is the imaginary unit, defined by the equation i = √-1.

The powers of i follow a specific cycle:

  • i1 = i
  • i2 = -1
  • i3 = -i
  • i4 = 1

After i to the power of 4, the cycle starts over, so the next powers will just repeat this pattern. Thus, calculating i4 results in the value of 1.

This cyclical nature of i means that no matter how high a power you go, you can always find its equivalent by reducing that power modulo 4. For instance:

  • i5 = i (because 5 mod 4 = 1)
  • i6 = -1 (because 6 mod 4 = 2)
  • i7 = -i (because 7 mod 4 = 3)
  • i8 = 1 (because 8 mod 4 = 0)

In summary, i4 equals 1, and understanding this can help you work with complex numbers more fluently.

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