A First Course in Complex Analysis · Problem 1.5.17

Complex Numbers — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · roots-of-unity

Problem

Show that a complex number

\zeta

satisfies

\zeta^n = 1

for some positive integer

n

if and only if

\zeta

is of the form

e^{2\pi i m/n}

for some integers

m

and

n > 0