1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inequality problem

  1. Nov 30, 2006 #1
    Sorry that i posted in the wrong topic, i'm kind of new here :D
    Hi this is my problem:

    if 0<|z|<1 and z_1 = -1/a - ((1-a^2)^(1/2))/a
    z_2 = -1/a + ((1-a^2)^(1/2))/a
    Then it is clear to me that |z_1|>1 since using triangle inequality we get that |z_1| =| -1/a - ((1-a^2)^(1/2))/a | >= |1/a| + something smaller than one but positiv, and since |1/a| >1 then |z_1| > 1

    But how to prove |z_2| < 1 since bye triangle inequality we kind of get the same thing |z_2| = | -1/a + ((1-a^2)^(1/2))/a | >= |1/a|+ |((1-a^2)^(1/2))/a| > 1 ???? This doesnt make sense at all!

    Please help me, i need this to a problem on an integral in complex analysis, which i'm preparing for my exam ;)

    thank you for your time!
  2. jcsd
  3. Dec 1, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    What exactly did you learn as "the triangle inequality"? Most people learn it as [itex]|a+ b|\le |a|+ |b|[/itex]. From that, if we let a= x- y, b= y we get
    [itex]|x-y+y|= |x|\le |x-y|+ |y|[/itex] so that [itex]|x-y|\ge |x|- |y|[/itex]. That second inequality is what you used. To prove the second part use the inequality [itex]|a+b|\le |a|+ |b|[/itex].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Inequality problem
  1. Inequality Problem (Replies: 5)

  2. Inequality problem (Replies: 3)

  3. Inequality problem (Replies: 4)

  4. Inequality problem (Replies: 0)

  5. Inequality problem (Replies: 4)