The image under mapping $w=(z+i)/(z-i)$, of the third quadrant?

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The title says it all. I am not sure how to approach this problem. The only related problems i have done is mapping a (unbounded)line /circle to a line/circle.

Regards Exatic

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Hints:

  • The third quadrant is bounded by the $x,y$ axes.
  • Möbius transformation preserve orientation, in the sense that the region to the left (right) of the line/circle is mapped onto the region to the left (right) of the line/circle in the image.