If n is 2, these numbers are 1 and -1. For 10 points each:
[10m] Name these numbers that, when raised to the power of a positive integer n, equal one. These numbers are sometimes named after the French mathematician Abraham de Moivre (“mwahv”).
ANSWER: roots of unity [accept nth roots of unity]
[10e] The sum of the n-th roots of unity for any n always equals this number. Any number multiplied by this number yields this number.
ANSWER: zero [or 0]
[10h] Adjoining a root of unity to the rationals is the definition of a cyclotomic one of these constructs, which is a ring where every non-zero element has a multiplicative inverse.
ANSWER: fields [accept cyclotomic fields; accept cyclotomic field extension; prompt on cyclotomic extension by asking “extension of what?”]
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