orthogonality in a complex vector space

[wary forge]

the book I am using says that in order for two complex vectors to be orthogonal $\real{\langle u,v \rangle} = 0$

[rain ibex]

martin(ping-me-when-reply)

[wary forge]

must it be the real part of the inner product?

if so, why?

or is this just more generalized than saying $\langle u,v \rangle = 0$ because if $\real{\langle u,v \rangle = 0} \rightarrow \langle u,v \rangle = 0$

[rain ibex]

martin(ping-me-when-reply)

[wary forge]

wait but that's not true

wait