Endomorphism/Normal/Sum with homothety/Exercise

Let ${\displaystyle {}V}$ be a finite-dimensional ${\displaystyle {}{\mathbb {K} }}$-vector space, endowed with an inner product, and let

${\displaystyle \varphi \colon V\longrightarrow V}$

denote a normal endomorphism. Show that also ${\displaystyle {}\varphi -\lambda \cdot \operatorname {Id} _{V}}$ is normal.