Mathematics, 20.11.2019 00:31 Gearyjames8
Let $z$ be a complex number, and let $n$ be a positive integer such that\[z^n = (z + 1)^n = 1.\]
a) prove that $|z| = |z+1| = 1$.
b) find the possible values of $z$ in exponential form.
c) prove that $n$ must be divisible by $6$.
Answers: 1
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Let $z$ be a complex number, and let $n$ be a positive integer such that\[z^n = (z + 1)^n = 1.\]
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