Complex Analysis: Theory and Applications · Problem 5.3.8

Elementary Functions — Howell & Matthews

Mathematics — Complex Analysis · complex-exponents-principal-value-product

Problem

Construct an example that shows that the principal value of

(z_1 z_2)^{\frac{1}{3}}

need not equal the product of the principal values of

z_1^{\frac{1}{3}}

and

z_2^{\frac{1}{3}}