A First Course in Complex Analysis · Problem 50

Integration — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · complex-exponentials

Problem

Prove that

\exp(b \log a)

is single valued if and only if

b

is an integer. (Note that this means that complex exponentials do not clash with monomials

z^n

, no matter which branch of the logarithm is used.) What can you say if

b

is rational?