Inner Product on Complex Vector Space

Question

Let $\left< . , .\right>$ denote an inner product on $V$ where $V \subseteq \mathbb{C}^n$. I'm having trouble understanding why

$$ \left< u, iv\right>i = \left< u, v\right> $$

Could someone possible shed some light on this for me?

Answer 1

$$ \langle u, iv \rangle i = i\int u \cdot \overline{iv}\ dx = i\int u \cdot \overline i \cdot \overline v\ dx = i \cdot (-i) \int u \cdot \overline v\ dx = \int u \cdot \overline v\ dx = \langle u, v \rangle $$