ⁿ√1 isn't just equal to 1! There are actually 𝑛 different complex numbers such that 𝑧ⁿ=1. Geometrically, these 'roots of unity' correspond to the 𝑛 different angles that when rotated 𝑛 times successively around the unit circle return to the same placepic.twitter.com/ifwVmxKlqi
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I have two questions: Why do you choose not to adhere to the convention and what does ⁿ√𝑧 denote in your unconventional notation? a set? a tuple? something else?
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I still remember in high school math class a kid told the teacher, "The square root of 9 [or whatever number it was] is plus or minus 3." The teacher said, "No, by convention it is only the positive root." (Your n = 2 case.)
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