Recent content by sweetvirgogirl

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    Riemann Mapping theorem

    so i know what it is (i think lol) ... but what are its applications?
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    Scharwz lemma

    f (z) = lamdba (a - z)/(1 - abar*z) |lambda| = 1; |a| <1 where f is any one-to-one analytic function mapping delta = {z:|z| < 1} onto itself set g(z) = (a - f(z))/(1-abar*f(z)) now they say that g is one-to-one analytic function mapping delta onto delta (why?) and g(0) = 0 and then they...
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    Scharwz lemma

    so the way book states it, for the sc. lemma to work, |f(z)| has to be less than or equal to 1 and and z has to be less than 1. However, the book seems to use the lemma in some problems even if one of the conditions is not satisfied ... any help with gretaly appreciated also ...if you could...
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    Openset / closedset / connected

    thats what i thought .... i wrote down "open" as my answer and the prof circles it and I dont think I got any points for it ... yes, i didnt write connected, but I should at least get half the points or something. oh well maybe he didnt gimme any credit, because I didnt explain why I think it's...
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    Openset / closedset / connected

    in that case ... wouldnt it be an open set? and it will be above real axis? (meaning the boundary is upper plane or lower plane? getting confused with terminology a little)
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    Linear fractional transformation

    how exactly do you determine that? coz the way i saw it ... -1 was on the line ... maybe i need some rest
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    Complex analysis - area inside a simple closed curve

    Let C be a simple closed curve. Show that the area enclosed by C is given by 1/2i * integral of conjugate of z over the curve C with respect to z. the hint says: use polar coordinates i can prove it for a circle, but i am not sure how to extend it to prove it for any given closed curve
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    Openset / closedset / connected

    {z^2: z = x+iy, x>0, y>0} i am a lil confused about the notation to represent the set ... i'm used to seeing {z: z = x+iy, x>0, y>0} but what effect does squaring z have? i thought the set was open simply because x>0 and y>0 ... but apprently i was wrong ... (or maybe not?) ... i...
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    Linear fractional transformation

    no we havent covered cross ratio in class yet. so i *sorta* get how to send a circle to a line ... ... the circle |z| = 1 and the line Re((1+i)w) = 0 ... so i sent 1 to infinity, -1 to 0 and i = -1 and i came up with i*(z+1)/(z-1) ... the book has the answer as (1-i)*(z+1)/(z-1) i...
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    Linear fractional transformation

    woopsie ... let's restart then ... I send i to infinity, -i to zero ... what about the third point? it has to do something with fixing orientation, right? how does that work? (like i know the third point can not be totally arbitrary like the first two points were, right?)
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    Linear fractional transformation

    oops typo ... i meant we could send i to infinity and -i to - infinity and then the third point? (-infinity and infinity are different, right?)
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    Complex analysis - maximum/modulus principle

    if i apply max/min modulus to both f and 1/f, then it means both f and 1/f dont have a local max/min ... so what does it tell me? i'm sorry ... i dunno if it's lack of confidence or what .. but i still dont see it
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    Complex analysis - maximum/modulus principle

    thats what i thought .... but i still have no insight about f having any zero inside lambda .... like i kinda see it visually ... like i know it makes sense ... but i got no clue how to "prove" it
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    Linear fractional transformation

    the way prof showed it in class ... he said pick three points on the circle and send it to three points on the line (or vice versa if we are trying to map a line to a cirle) ... but i am not sure how do i know what those three points are going to map to .... on a circle |z| = 1, we could...
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    Complex analysis - LFT

    what do i do with cases infinity/infinity and/or 0/0?
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