[Home]ExtendedComplexPlane

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Just don't ask.

TE-Complex plane?  ETE-Complex plane?

Isn't this just a complex plane with weightings attached?

Oh, silly me.  It's the complex plane with an extra point for infinity.  Silly me.  (This point is, of course, represented as a line around the circumference of the plane.  No, you can't have a circumference around something infinite, but it makes it easier to draw.  Anyway, then you can contort the plane into an 'almost sphere' with this final point making it a real sphere - the RiemannSphere.

Whahey!  I remembered something!

(Unless I remembered wrong, and the extended complex plane is really the complex plane with a line cutting out the zero point - in a display of ironic naming practices.)

Hi all. Consider the extended complex plane as `the complex plane union the point at infinity'. This implies that the mapping z -> 1/z maps the extended plane to the extended plane - the points at zero and infinity are interchanged. However, on a normal complex plane, this would not be the case.

The extended plane is a useful thing to consider for nice topological reasons and analytical reasons, eg the RiemannSphere.

See, I told you not to ask :-) -- Hawk

Unfortunately you neglected the high MathMo quotient around here -- Senji



CategoryMaths CategoryGeometry CategoryPlace ;)

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