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Modulus of f(z)

  1. May 24, 2012 #1
    For expressions like:

    f(z) = (1+z2)/(1+z4) how does one write the modulus of that in terms of lzl?
     
  2. jcsd
  3. May 24, 2012 #2

    tiny-tim

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    hi aaaa202! :smile:
    i don't really understand the question :redface:

    how does one write eg the modulus of 1+z2 on its own in terms of lzl only ?? :confused:
     
  4. May 24, 2012 #3
    Well I want to find lf(z)l and show that lzllf(z)l goes to 0 as lzl goes to infinity. So wouldn't I need to write the function above in terms of lzl, multiply by lzl, and show that it goes to zero?
     
  5. May 24, 2012 #4

    tiny-tim

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    in that case, write z = re :wink:
     
  6. May 24, 2012 #5
    hmm yes okay. So in that case i would for instance get:

    (1+lzl2ei2θ)/(1+lzl4ei4θ). But still that doesnt really give me the modulus for the whole expression?
     
  7. May 24, 2012 #6

    tiny-tim

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    ok, so multiply by |z| and then let |z| -> ∞ …

    what difference do the θ terms make? :wink:

    (btw, we normally write 2iθ rather that i2θ)
     
  8. May 24, 2012 #7
    oh well but the expression above is f(z) not lf(z)l = mod(f(z)), and I wanted to show that lzllf(z)l -> 0 as lzl->∞..

    Edit: Oh well if f(z) goes to zero then surely lf(z)l does too.. So nevermind, unless you can have lf(z)l->0 even though f(z) doesn't? Nah that wouldn't make sense right..?
     
    Last edited: May 24, 2012
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