Measure, Integration & Real Analysis · Problem 6B.1

Banach Spaces — Sheldon Axler

Mathematics — Measure Theory · complex-numbers-reciprocal

Problem

Show that if

a, b \in \mathbf{R}

with

a + bi \neq 0

, then

\frac{1}{a + bi} = \frac{a}{a^2 + b^2} - \frac{b}{a^2 + b^2}\, i.