Assuming $x,y\in\mathbb C^n$,consider:
$f(x,y)=\sup_{θ,φ}\{||e^{i θ }x+ e^{i φ }y||^2: θ,φ\in\mathbb R\}$
Which of the following is/are correct?
1.$ f(x,y)$≤$||x||^2+||y||^2+2|(x,y)|$
2. $f(x,y)$= $||x||^2+||y||^2+2Re(x,y)$
3. $f(x,y)$= $||x||^2+||y||^2+2|(x,y)|$
4. $f(x,y)$> $||x||^2+||y||^2+2|(x,y)|$
How can I solve this problem ,I am completely stuck on it . can anyone help me?thanks