In general is it true that $||v-u||= ||u-v||$? In general is it true that $||v-u||= ||u-v||$?
Here, I am assuming that $u$ and $v$ are elements of an inner product space. I am unable to come up with a proof in the complex vector space case.

\begin{align}
||u-v|| &= \sqrt{\langle u-v,u-v \rangle}  \\
    &= \sqrt{-1 \langle v-u,u-v \rangle}  \\
    &= \sqrt{-1 \overline{-1}\langle v-u,v-u \rangle}  \\
    &= \sqrt{\langle v-u,v-u \rangle}  \\
    &= ||v-u||
\end{align} because $\overline{-1} = -1$ and $-1 \cdot -1 = 1$.
