Commit 5beffa88 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 40426e9f
Pipeline #15866 canceled with stage
...@@ -508,24 +508,14 @@ $`\forall \alpha \in \mathbb{R}\;,\,`$ **$`\large{exp{\,\alpha} = cos \,\alpha + ...@@ -508,24 +508,14 @@ $`\forall \alpha \in \mathbb{R}\;,\,`$ **$`\large{exp{\,\alpha} = cos \,\alpha +
* $`\underline{A}=A\,e^{\,i\,\varphi}`$ : amplitude complexe. * $`\underline{A}=A\,e^{\,i\,\varphi}`$ : amplitude complexe.
* $`\underline{A}^{\ast}=A\,e^{\,-i\,\varphi}`$ : amplitude complexe conjuguée. * $`\underline{A}^{\ast}=A\,e^{\,-i\,\varphi}`$ : amplitude complexe conjuguée.
<br> <br>
$`\begin{array} $`\begin{align}
\large{\mathbf{\color{brown}{\quad \sqrt{\underline{A}\,\underline{A}^{\ast}}}}} &= \sqrt{A\,e^{\,i\,\varphi}\times A\,e^{\,-i\,\varphi}}\\ \large{\mathbf{\color{brown}{\quad \sqrt{\underline{A}\,\underline{A}^{\ast}}}}} &= \sqrt{A\,e^{\,i\,\varphi}\times A\,e^{\,-i\,\varphi}}\\
\\ \\
&= \sqrt{A^2\,e^{\,i\,\varphi}\,e^{\,-i\,\varphi}} = \sqrt{A^2\,e^{\,(i-i)\,\varphi}}\\ &= \sqrt{A^2\,e^{\,i\,\varphi}\,e^{\,-i\,\varphi}} = \sqrt{A^2\,e^{\,(i-i)\,\varphi}}\\
\\ \\
&= \sqrt{A^2\,e^0}=\sqrt{A^2} = \vert\,A\,\vert^2\\ &= \sqrt{A^2\,e^0}=\sqrt{A^2} = \vert\,A\,\vert^2\\
\\ \\
\large{\mathbf{\color{brown}{&= A^2}}}\end{array}`$ &\large{\mathbf{\color{brown}{= A^2}}}\end{align}`$
<br>
$`\begin{array}
\large{\mathbf{\color{brown}{\quad \sqrt{\underline{A}\,\underline{A}^{\ast}}}}} &= \sqrt{A\,e^{\,i\,\varphi}\times A\,e^{\,-i\,\varphi}}\\
\\
&= \sqrt{A^2\,e^{\,i\,\varphi}\,e^{\,-i\,\varphi}} = \sqrt{A^2\,e^{\,(i-i)\,\varphi}}\\
\\
&= \sqrt{A^2\,e^0}=\sqrt{A^2} = \vert\,A\,\vert^2\\
\\
&\large{\mathbf{\color{brown}{= A^2}}}\end{array}`$
......
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