Can you help me find an example for $\,u,v \in \Bbb C^2\,$ unit vectors that $\langle u,v\rangle\neq 0$ and $\|u+v\|=\sqrt 2$
$u,v$ over $C^n$ and we know that $\|u\|=\|u+v\|=\|u-v\|$ need to prove $v=0$
after I opened every thing I got to this: $4Re(\langle u,v\rangle)=\langle u,u\rangle$ but I don't see how it helps me.