I've attached the picture of a question presented to me in an assignment. The solution begins with an equality, 'the general result', that I cannot find anywhere. I have looked across my book, scripts we've been provided, and online. Can somebody please explain where it comes from?
Just write $(v-z)$ as $(v-v^{*}) +(v^{*}-z)$ and use the identity $\|a+b\|^{2}=\|a\|^{2}+\|b\|^{2}+2 Re \langle a, b \rangle$.
$\|v-z\|^{2}=\|(v-v^{*}) +(v^{*}-z)\|^{2}=\|v-v^{*}\|^{2}+\|v^{*}-z\|^{2}+2 Re \langle (v-v^{*}), (v^{*}-z) \rangle$. All you have to do now is to rearrange the terms.