What is i ¹²³⁴⁵⁶⁷⁸⁹⁰?

3 Answers

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  • 1 month ago

    Find 1234567890 mod 4...

    then look at the pattern

    i^1 = sqrt(-1)

    i^2 = -1

    i^3 = i^2 * i = -1*i = -i

    i^4 = i^2 * i^2 = (-1) * (-1)

    so 1234567890 mod4 = 2

    hence i^1234567890 = i^2 = -i

  • 1 month ago

    "i" is an imaginary number that loops every 4 times through:

    i⁰ = 1

    i¹ = i

    i² = -1

    i³ = -i

    So if the exponent is a multiple of 4, then the result is 1.  Whatever the remainder is after dividing by 4 will tell us which of the other 3 possible options it is.

    So divide and check the remainder:

    1234567890 / 4 = 308641972 R 2

    Since the remainder is 2, your expression simplifies to:

    -1

  • Jim
    Lv 7
    1 month ago

    Since it's even, I would surmise it's -1

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