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How do you evaluate i to large powers such as i^1992, i^1993, and i^2000 without a calculator?

  • math -

    since i^2 = -1, i^4 = 1.

    So, divide the power by 4, since every factor of i^4 is just 1.

    You will be left with one of the following:

    i^0 = 1
    i^1 = i
    i^2 = -1
    i^3 = -i

    For example, i^913 = i^1 = i

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