(i^4)^(1/2)

...
i-2 = 1/i2 = 1/-1 = -1
i-1 = 1/i * i/i = i/i2 = i/-1 = -i
i0 = 1
i1 = i
i2 = -1
i3 = i2 * i = -1 * i = -i
i4 = i2 * i2 = -1 * -1 = 1
i5 = i4 * i = 1 * i = i

i1/2?
√(i) = √(i5)
√(i) = √(i4) * √(i)
√(i) = √(i2) * √(i2) * √(i)
√(i) = i * i * √(i)
√(i) = -1 * √(i)

Divide both sides by √(i), and you get 1 = -1.

2 Responses to “(i^4)^(1/2)”

  1. On March 29th, 2004 at 22:41:29, Schlueterica Said:

    Solution to the puzzleIf you haven’t seen the √(i^4) puzzle, I recommend you go check it out. It’s good stuff. Read on for the answer.

  2. On April 1st, 2004 at 08:59:28, TommyBlack Said:

    square root of i squared is plus or minus i, isn’t it? so you get alternate answers of 1=-1 or 1=1. and you pick the right one.

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