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
    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!
    Garret
     
  2. jcsd
  3. Nov 30, 2006 #2

    berkeman

    User Avatar

    Staff: Mentor

    Sorry, what is a?
     
  4. Dec 2, 2006 #3

    SGT

    User Avatar

    I suppose that the first equation should be 0 <|a|<1.
    The second term of the equations for [tex]z_1[/tex] and [tex]z_2[/tex] has the same sign as [tex]\frac{1}{a}[/tex].
    When both terms have the minus sign, you are adding the moduli and clearly the modulus of the result is greater than 1.When the first is negative and the second positive you subtract the moduli. It remains to show that the modulus of the result is smaller than 1.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



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

  2. Units problem (Replies: 2)

Loading...