A Root-of-Unity Shift

★ 6/10complex numbers Modular Arithmetic Casework

Problem

A complex number $z$ satisfies $|z| = 1$ and

z^n = z + \sqrt{2}.

Find the least positive integer $n$ for which such a $z$ exists.

Answer

Solution

Difficulty	6/10
Topics	complex numbers, Modular Arithmetic, Casework

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