Art of Problem Solving

User:Temperal/The Problem Solver's Resource Competition: Difference between revisions

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<cmath>
\begin{align*}
\begin{align*}
     |\langle (z,i), (i,w)\rangle| &\leq ||(z,i)||||(i,w)|| \\
     |\langle (z,i), (i,w)\rangle| &\leq ||(z,i)||||(i,w)|| \\
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     \frac{|z + w|^2}{|z|^2 + 1} &\leq |w|^2 + 1
     \frac{|z + w|^2}{|z|^2 + 1} &\leq |w|^2 + 1
\end{align*}|
\end{align*}|
</cmath>

Revision as of 12:47, 8 October 2024

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