I'm working on linear transformation and trying to answer :
Let E and F be two vector-spaces on $\mathbb{C}$ and $L:E \rightarrow F$ an application such as :
$\forall u,v \in \ E, L(u+v)=L(u)+L(v) $
$\forall u \ \in \ E, \forall \alpha \ \in \ \mathbb{R}, L(\alpha u)=\alpha L(u)$
Prove that $L$ is a linear transformation if and only if $L(iu)=iL(u)$
I have tried taking $u=(x1,y1)$ and $v=(x2,y2)$ but did not manage to prove it.