User:Temperal/The Problem Solver's Resource Competition

< User:Temperal
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\begin{align*}     |\langle (z,1), (1,\overline{w})\rangle| &\leq ||(z,1)||||(1,\overline{w})|| \\     |z + w|^2 &\leq (|z|^2 + 1)(|w|^2 + 1) \\     \frac{|z + w|^2}{|z|^2 + 1} &\leq |w|^2 + 1 \end{align*}|