User:Temperal/The Problem Solver's Resource Competition

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\begin{align*}     |\langle (z,i), (-i,\overline{w})\rangle| &\leq ||(z,i)||||(-i,\overline{w})|| \\     |iz + iw|^2 &\leq (|z|^2 + 1)(|w|^2 + 1) \\     \frac{|z + w|^2}{|z|^2 + 1} &\leq |w|^2 + 1 \end{align*}|