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!

Euler's Formula Contradiction?

  1. May 9, 2015 #1

    TheDemx27

    User Avatar
    Gold Member

    I've been using euler's formula now more than I have in the past, (using it for circuit analysis stuff), and so its been floating around in my head a bit more.

    Say you have [itex]e^{2πi}=1[/itex] and you take the natural log of both sides.

    [itex]\log_e( e^{2πi})=\log_e(1)[/itex]
    [itex]2πi=0[/itex]
    uhhhhh... :confused:
     
  2. jcsd
  3. May 9, 2015 #2
    The problem is that you are using the real natural logarithm, which is the inverse of the real exponential function [itex]e^x[/itex]. You need to use the complex logarithm.
     
  4. May 9, 2015 #3

    TheDemx27

    User Avatar
    Gold Member

    Ah, thankyou.
     
  5. May 9, 2015 #4
    The general equation is ##e^{\pm 2ni\pi}=1##
    The function ##e^{ix}## has periods of ##2\pi##, just as the trigonometric functions have periods of ##2\pi##
    [i.e. although ##sin(2\pi)=sin(0),\ 2\pi\neq0##]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Euler's Formula Contradiction?
  1. Eulers Formula (Replies: 11)

  2. Euler's Formula Proof (Replies: 15)

Loading...