Let be a complex number satisfying the equation

MATHEMATICS · Subjective · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Let

z

be a complex number satisfying the equation

z^2 - (3+i)z + \lambda + 2i = 0

, where

\lambda \in \mathbb{R}

and

i = \sqrt{-1}

. Suppose the equation has a real root, find the non-real root.