The roots of unity of ⁵√1pic.twitter.com/00U2Yq8A34
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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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Note: There is a bit of notational convention i didn't adhere to. The ⁿ√ symbol is usually reserved for the 'principal root' of 𝑧 so that ⁿ√ denotes a single valued function of 𝑧 .pic.twitter.com/PHW17NNoeu
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i don’t understand but this is how washing machines work right
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most, but not all
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wait really??? COOL.
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I am so annoyed that we're not supposed to teach this in high school. I try to get it into the end of algebra II, because it ties exponents and trig functions (and series and transformations) all together. But it's not actually part of the standards.
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Round and round it goes, where it stops? Pretty trivial to calculate actually.
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This was my favorite part of the complex numbers chapter in the Math Methods course I'm teaching! Seeing students see this for the first time is priceless!
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Thanks. Twitter will use this to make your timeline better. UndoUndo
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Nice. One remark: ⁿ√1 typically indicates one specific choice (the positive n-th root, that is 1, in this case, as standard). It is better to say, as you do later in your tweet, that there are many numbers z whose n-th power gives 1.
Thanks. Twitter will use this to make your timeline better. UndoUndo
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