Solution
= Solution
Expand both squared <norms> using sesquilinearity and <conjugate symmetry>. Their mixed terms $\langle u,v\rangle+\langle v,u\rangle$ appear with opposite signs and cancel. Hence
$$
\boxed{\|u+v\|^2+\|u-v\|^2=2\|u\|^2+2\|v\|^2,}
$$
the <parallelogram identity>.