Maximum modulus principle
General · Mathematics
Study notes
Q: Where does |z²+1| attain its maximum on |z| ≤ 1? Can it be interior? f(z) = z²+1: analytic, non-constant. Maximum modulus: on BOUNDARY |z| = 1 (never interior!)! |e^(i2θ)+1| = 2|cos θ|: max 2 at z = ±1. Interior: |f(0)| = 1 < 2 ✓ (no interior max!)!