<s>[INST] If $a^2+b^2\leq 1$ and $c^2+d^2<1$, then $a^2+b^2+c^2+d^2\leq 1+a^2c^2+b^2d^2+b^2c^2+a^2d^2$ If $a^2+b^2\leq 1$ and $c^2+d^2<1$, then $a^2+b^2+c^2+d^2\leq 1+a^2c^2+b^2d^2+b^2c^2+a^2d^2$
Is this true? This simple algebra should hold in order to finish my problem on Complex Analysis. Computing few numbers suggests that this is true, but I don't seem to be able to prove it.
 [/INST] Hint: If $x$, $y\le1$ then $$0\le(1-x)(1-y)=1-x-y+xy$$
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