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Complex inequality

  1. Nov 3, 2009 #1
    How to prove the following inequality: for complex z such that Re z < 0 :

    [tex]\left| e^z-1\right| < \left| z\right|[/tex] ?
     
  2. jcsd
  3. Nov 3, 2009 #2
    use the identities

    [tex]\left|z\right|^{2}=z\bar{z}[/tex]

    and

    [tex]\bar{e^{z}}=e^{\bar{z}}[/tex]

    since both sides of the inequality are positive
    you can square it up
     
  4. Nov 4, 2009 #3
    What next?
     
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