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Math Help - Two question from complex analysis

  1. #1
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    1. Find the general form of bilinear
    mapping that maps the upper halfplane H^+=\{z : Imz >0\}
    to yourself.

    2. Prove that for all R: R>0, n \in N (large enough),
    all zeros of polynom
    p_n(z)=\frac{1}{n!}z^n + ... + \frac{1}{2!}z^2 + 1
    are in \{z \in \mathbb{C}: |z| > R\}

    Coment: For 2. p_n -> e^z, and... ?

    New question:

    H^+ = \{z : Im z>0\}.
    f(z)=z^5.

    Now, f(H^+) = \{ z= r e^{i \theta} : r >0, 0 < \theta < 5\pi\} = \mathbb{C} \ \{x \leq 0\}
    or f(H^+) = \{z= r e^{i\theta} : r >0, 0 < \theta < \pi\} ?

    Is needed mod 2\pi ?
    Last edited by mr fantastic; April 25th 2010 at 04:11 AM. Reason: Merged posts
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