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gaspard/inv_conj.tex

Last active September 21, 2024 12:25
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conjugué de l'inverse et inverse du conjugué
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inv_conj.tex
\begin{align}
\overline{z_1-z_2}^{-1} &\\
& = \overline{(-1-i)-(-1+i)}^{-1} \\
& = \overline{(-1-i)+(+1-i)}^{-1} \\
& = \overline{(-2i)}^{-1} \\
& = (2i)^{-1} \\
& = \frac{1\cdot(-2i)}{(2i)\cdot(-2i)} \\
& = \frac{-2i}{-4i^2} \\
& = \frac{-2i}{4} \\
& = -\frac{1}{2}i \\
\end{align}
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gaspard commented Sep 21, 2024

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