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Thread: some algebra with complex numbers

  1. #1
    Ant
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    some algebra with complex numbers

    Let $\displaystyle c,a \in \mathbb{C}$ be constants, let $\displaystyle n,m \in \mathbb{N}$, and let $\displaystyle z$ be a complex variable.

    Is it true that:

    $\displaystyle \bigl(c(|z|+1)^n +|a| \bigr) \ |z|^m = c_0 (|z|+1)^{n-m} $

    For a suitable constant $\displaystyle c_0$?

    It would be very helpful if this were true for a proof I'm trying to figure out...

    Thanks
    Last edited by Ant; Apr 21st 2013 at 04:26 PM.
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  2. #2
    MHF Contributor
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    Re: some algebra with complex numbers

    It doesn't seem like it would be possible - if $\displaystyle |z|$ is large, the left-hand side grows like $\displaystyle |z|^{n+m}$ and the right-hand side grows like $\displaystyle |z|^{n-m}$.

    - Hollywood
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