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Counting problem with Mobieus function

  1. Oct 29, 2009 #1
    1. The problem statement, all variables and given/known data
    How can you get from this
    [tex] \frac {z(i-1) +i +1} {z(1-i) +i +1} [/tex]
    to this
    [tex] = \frac { z-1 } {-z -i} [/tex]
    ?

    3. The attempt at a solution

    SageMath does not simplify the result any further from the beginning.
    The equivalence is based on some high Math.

    I am not sure how you can deduce the equivalence.
     
  2. jcsd
  3. Oct 29, 2009 #2
    The expressions are not equal. Try z = 0, you get 1 in the first expression and -i in the second.
    The valid equation is:

    [tex]
    \frac {z-i} {-z-i} = \frac {z(i-1) +i +1} {z(1-i) +i +1}
    [/tex]

    To check that just multiply and divide the LHS by (i - 1)
     
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