1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Whats wrong here?

  1. May 1, 2006 #1
    [tex]e^{iz}-e^{-iz} = 4i[/tex]
    [tex]e^{2iz}-4ie^{iz} = 1[/tex]
    [tex]iz \ln (e^{iz}-4i) = 0[/tex]
    [tex] z=0[/tex]

    when solving it by
    [tex]w = e^{iz}[/tex]
    [tex]w^2-4wi-1 = 0[/tex]
    i get one more solution, why is the first way not as good as the second way?
  2. jcsd
  3. May 1, 2006 #2


    User Avatar
    Science Advisor

    ln(ab)= ln(a)+ ln(b), not ln(a)*ln(b).

    If [tex]e^{2iz}-4ie^{iz} = 1[/tex]
    then [tex]e^{iz}(e^{iz}- 4i)= 1[/tex]
    so [tex]iz+ ln(e^{iz}- 4i)= 0[/tex]
    NOT [tex]iz \ln (e^{iz}-4i) = 0[/tex]
  4. May 2, 2006 #3
    hehe, right, that was a dumb mistake :biggrin:
    thank you for pointing it out.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook