Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quick question about conjugates

  1. Sep 21, 2010 #1
    Hi I have a parametrisation of the unit circle
    z = cos(t) + isin(t) = e^(it)
    now i guess that the conjugate of that is the same but with a negative coefficient on the imaginary part, namely:
    conj z = cos(t) - isin(t)
    How does that extend to the e^(it) form? is the following true:
    cos(t) - isin(t) = e^(-it)

    Last edited: Sep 21, 2010
  2. jcsd
  3. Sep 21, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    [tex]e^{-it}=\cos(-t)+i\sin(-t)[/tex]. cosine is an even function, an sine is an odd function, so

  4. Sep 23, 2010 #3
    nice, thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook