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!

Complex numbers

  1. Oct 22, 2012 #1
    Can someone please prove the formulas:

    The real part of z= 1/2(z+z*)
    And the imaginary part of z= 1/2i(z-z*)

    I can't understand why it is like this. Could someone please give me the proof?
     
  2. jcsd
  3. Oct 22, 2012 #2
    What are ##z## and ##z^*## in terms of their real and imaginary parts?
     
  4. Oct 22, 2012 #3

    I write [itex]\,\overline z\,[/itex] instead of your z*. Put

    $$z=x+iy\,\,,\,\,x,y\in \Bbb R\Longrightarrow \,\,Re(z)=x\,\,,\,\,Im(z)=y\Longrightarrow$$

    $$z+\overline z=x+iy+x-iy=2x\;\;,\;\;z-\overline z=x+iy-(z-iy)=2yi$$

    Now end the exercise.

    DonAntonio
     
  5. Oct 22, 2012 #4
    So 1/2 2x = re part = 1/2(z+z*)
    And 1/2i 2yi= Im part= 1/2i(z-z*)

    Thanks!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...