Le-plan-complexe-est-rapporte-a-un-repe-re-orthornorme-directe-0-e-1-e-2-On-note-A-et-B-les-points-d-affixes-respectives-i-et-2i-Soit-f-l-application-du-plan-prive-de-A-dans-l

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Question Number 98638 by Ar Brandon last updated on 15/Jun/20

$$\mathrm{Le}\mathrm{plan}\mathrm{complexe}\mathrm{est}\mathrm{rapport}\acute{\mathrm{e}}\stackrel{`}{\mathrm{a}}\mathrm{un}\mathrm{rep}\stackrel{`}{\mathrm{e}re}$$$$\mathrm{orthornorme}\mathrm{directe}(0,{\overrightarrow{\mathrm{e}}}_1,{\overrightarrow{\mathrm{e}}}_2).\mathcal{O}\mathrm{n}\mathrm{note}\mathrm{A}\mathrm{et}\mathrm{B}\mathrm{les}$$$$\mathrm{points}{\mathrm{d}}^{\prime }\mathrm{affixes}\mathrm{respectives}\mathbf{i},\mathrm{et}2\mathbf{i}.\mathrm{Soit}\mathrm{f},{\mathrm{l}}^{\prime }\mathrm{application}$$$$\mathrm{du}\mathrm{plan}\mathrm{priv}\acute{\mathrm{e}}\mathrm{de}\mathrm{A}\mathrm{dans}\mathrm{lui}-\mathrm{m}\widehat{\mathrm{e}me}\mathrm{qui}\stackrel{`}{\mathrm{a}}\mathrm{tout}\mathrm{point}$$$$\mathrm{M}{\mathrm{d}}^{\prime }\mathrm{affixe}\mathrm{z}\mathrm{distincte}\mathbf{i}\mathrm{associe}\mathrm{le}\mathrm{point}\mathrm{M}{\mathrm{d}}^{\prime }\mathrm{affixe}$$$${\mathbf{z}}^{\prime }\mathrm{definie}\mathrm{par}:{\mathrm{z}}^{\prime }=\frac{2\mathrm{z}-\mathrm{i}}{\mathrm{iz}+1}$$$$1\mathrm{\setminus }\mathrm{Soit}\mathrm{z}\ne \mathrm{i}$$$$\mathrm{a}\mathrm{\setminus }\mathrm{On}\mathrm{pose}\mathrm{z}-\mathrm{i}={\mathrm{re}}^{\mathrm{i}\theta }.\mathcal{I}\mathrm{nterpreter}\mathrm{g}\acute{\mathrm{e}ometriquement}\mathrm{r}\mathrm{et}\theta$$$$\stackrel{`}{\mathrm{a}}{\mathrm{l}}^{\prime }\mathrm{aide}\mathrm{des}\mathrm{points}\mathrm{A}\mathrm{et}\mathrm{M}.$$

Commented by IE last updated on 15/Jun/20

$$\mathrm{hello}\mathrm{Brandon}!$$

Commented by Ar Brandon last updated on 15/Jun/20

Hello ��

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