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ι 1 ⋅ ι 2 ⋅ ι 3 … ι 1 0 0 = ι 1 + 2 + 3 … + 1 0 0 = ι 2 1 0 0 × 1 0 1 = ι 5 0 5 0 = ι 2 = − 1 .
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this is weird solution, but shared any ways. note that i and its powers are roots of x 4 − 1 = 0 . by vietas the product of four taken at a time is -1. we are multiplying minus one 25 times, so the answer is -1.