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!

Disprooving Euler

  1. Jul 3, 2012 #1
    I was messing around with Euler’s Identity and I think I accidently disproved it. I would like someone to check my math to make sure I didn’t make any rookie mistakes.

    [tex]
    \begin{array}{l}
    e^{\pi i} + 1 = 0 \\
    e^{\pi i} = - 1 \\
    \left( {e^{\pi i} } \right)^2 = \left( { - 1} \right)^2 \\
    e^{2\pi i} = 1 \\
    \ln \left( {e^{2\pi i} } \right) = \ln \left( 1 \right) \\
    2\pi i = 0 \\
    \frac{{2\pi i}}{{\pi i}} = \frac{0}{{\pi i}} \\
    2 = 0 \\
    \end{array}
    [/tex]
     
  2. jcsd
  3. Jul 3, 2012 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    So, how did you define the logarithm on complex numbers??
     
  4. Jul 3, 2012 #3

    mathman

    User Avatar
    Science Advisor
    Gold Member

    ln(1) = 2kπi, where k is any integer. ln is a multivalued function.
     
  5. Jul 3, 2012 #4


    What gives you away as a rookie is the title of your post, not your mathematics...which are also wrong.

    Perhaps you'll be interested in reading about the complex logarithmic function's definition...

    DonAntonio
     
  6. Jul 3, 2012 #5

    tony873004

    User Avatar
    Science Advisor
    Gold Member

    edit: student posted under my account
     
  7. Jul 3, 2012 #6
    Thank you, DonAntonio, mathman and micromass, I thought that was what my error was, but I wasn't sure. You see, I haven't yet taken a course in which I learn even the basics of complex numbers, so my knowledge in that area is rather lacking.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Disprooving Euler
  1. Euler sum (Replies: 5)

  2. Euler's Method (Replies: 2)

  3. Eulers Formula (Replies: 11)

  4. Euler's number (Replies: 7)

Loading...