Complex Analysis: Theory and Applications · Problem 1.5-proof

Complex Numbers — Howell & Matthews

Mathematics — Complex Analysis · quadratic-formula-complex

Problem

Prove Theorem 1.5 (Quadratic formula): The equation

az^2 + bz + c = 0

has

\left\{\frac{-b+(b^2-4ac)^{\frac{1}{2}}}{2a}\right\}

as its solution set for

z

, where by

(b^2 - 4ac)^{\frac{1}{2}}

we mean all distinct square roots of that expression.