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Question Number 169918 by pticantor last updated on 12/May/22

A={z∈C: 2<∣z∣<4}  fine log(A)  where log is complex logaritmique

$${A}=\left\{\boldsymbol{{z}}\in\mathbb{C}:\:\mathrm{2}<\mid\boldsymbol{{z}}\mid<\mathrm{4}\right\} \\ $$ $$\boldsymbol{{fine}}\:\boldsymbol{{log}}\left(\boldsymbol{{A}}\right) \\ $$ $$\boldsymbol{{where}}\:\boldsymbol{{log}}\:\boldsymbol{{is}}\:\boldsymbol{{complex}}\:\boldsymbol{{logaritmique}} \\ $$

Answered by pticantor last updated on 12/May/22

besoin d′aide please!!

$$\boldsymbol{{besoin}}\:\boldsymbol{{d}}'\boldsymbol{{aide}}\:\boldsymbol{{please}}!! \\ $$

Answered by Mathspace last updated on 12/May/22

what mean logA ...

$${what}\:{mean}\:{logA}\:... \\ $$

Commented bypticantor last updated on 13/May/22

log A Is image of A by the logarithmic′fonction  and A is the ring   or   f:A→C       z↣log(z)  find log(A)

$$\boldsymbol{{log}}\:\boldsymbol{{A}}\:{Is}\:{imag}\boldsymbol{{e}}\:\boldsymbol{{of}}\:\boldsymbol{{A}}\:{by}\:{the}\:{logarithmic}'{fonction} \\ $$ $${and}\:{A}\:{is}\:{the}\:{ring}\: \\ $$ $${or}\: \\ $$ $$\boldsymbol{{f}}:{A}\rightarrow\mathbb{C} \\ $$ $$\:\:\:\:\:{z}\rightarrowtail{log}\left({z}\right) \\ $$ $${find}\:{log}\left({A}\right) \\ $$

Answered by Mathspace last updated on 13/May/22

if z=re^(iθ)  ⇒∣z∣=r⇒2<r<4  and logz=logr+i(θ+2kπ) ⇒  logA={logr+i(θ+2kπ) /k∈Z}  une determination principale est  logr+iθ     −π<θ<π

$${if}\:{z}={re}^{{i}\theta} \:\Rightarrow\mid{z}\mid={r}\Rightarrow\mathrm{2}<{r}<\mathrm{4} \\ $$ $${and}\:{logz}={logr}+{i}\left(\theta+\mathrm{2}{k}\pi\right)\:\Rightarrow \\ $$ $${logA}=\left\{{logr}+{i}\left(\theta+\mathrm{2}{k}\pi\right)\:/{k}\in{Z}\right\} \\ $$ $${une}\:{determination}\:{principale}\:{est} \\ $$ $${logr}+{i}\theta\:\:\:\:\:−\pi<\theta<\pi \\ $$ $$ \\ $$

Commented bypticantor last updated on 13/May/22

je crois que vous avez juste donner  la definition du logarithme complex!  mais on me demande la nature de log(A) et le   tracage de la courbe

$$\boldsymbol{{je}}\:\boldsymbol{{crois}}\:\boldsymbol{{que}}\:\boldsymbol{{vous}}\:\boldsymbol{{avez}}\:\boldsymbol{{juste}}\:\boldsymbol{{donner}} \\ $$ $$\boldsymbol{{la}}\:\boldsymbol{{definition}}\:\boldsymbol{{du}}\:\boldsymbol{{logarithme}}\:\boldsymbol{{complex}}! \\ $$ $$\boldsymbol{{mais}}\:\boldsymbol{{on}}\:\boldsymbol{{me}}\:\boldsymbol{{demande}}\:\boldsymbol{{la}}\:\boldsymbol{{nature}}\:\boldsymbol{{de}}\:\boldsymbol{{log}}\left(\boldsymbol{{A}}\right)\:{e}\boldsymbol{{t}}\:\boldsymbol{{le}}\: \\ $$ $$\boldsymbol{{tracage}}\:\boldsymbol{{de}}\:\boldsymbol{{la}}\:\boldsymbol{{courbe}} \\ $$

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