Stuck with linear algebra proof! Who show $\langle ix,y\rangle = i\langle x,y\rangle$?

Stuck with linear algebra proof! Who show $\langle ix,y\rangle = i\langle
x,y\rangle$?

Assume $\langle x,y\rangle =
1/4(\|x+y\|^2-\|x-y\|^2+i\|x+iy\|^2-i\|x-iy\|^2)$. If $\|\|$ satisfy the
parallelogram equation it is possible to show that $\langle x,y\rangle$
defines an inner product. I showed it for the real case. I wanted to prove
$i\langle x,y\rangle =\langle ix,y\rangle$ but fail. How to prove it?