This issue of infinity (undefined?) keeps coming up in the following problems.(adsbygoogle = window.adsbygoogle || []).push({});

For example, the following question:

Computer the image of the sector [itex]0 \leq r \leq 1, 0 \leq \theta \leq \pi[/itex], under the map ln(z).

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So I first graphed this thing in the x,y (z-plane) and obviously we get a half circle with radius 1, above/including x-axis.

Then I looked at the following points. A=0, B=1, C=i, D=-1. Then if we map them under [itex]w= ln(z)[/itex] we get,

A' = w(A)= ln(A) = ln(0) = ?

B' = ln(1) = 0

C' = ln(i) = [tex]i \frac{\pi}{2}[/tex]

D' = ln(-1) = [tex]i \pi[/tex]

If we then look at each segment, and map them under w, well I know what to do with everything but the parts that involve, or go though A. But the whole infinity, or undefined, issue bugs me.

Any ideas? Thanks.

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# Conformal Maps

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