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!

Finding unit vector

  1. Mar 12, 2013 #1
    I want to find the unit vector of ## \vec E= \hat x A\;+\;\hat y Be^{j\phi}##

    ##\hat E=\frac {\vec E}{|\vec E|}##

    From my work: ##|\vec E|=\sqrt{A^2+(Be^{j\phi})^2}##

    My question is what is ##(Be^{j\phi})^2##?

    Do I substitude ##e^{j\phi}=\cos \phi +j\sin \phi##? So ##(Be^{j\phi})^2=B^2[(\cos\phi+j\sin\phi)(\cos\phi-j\sin\phi)]\;=\;B^2(\cos^2\phi+\sin^2\phi)\;=\;B^2##

    ##\Rightarrow\;|\vec E|=\sqrt{A^2+(Be^{j\phi})^2}\;=\;\sqrt{A^2+B^2}## and

    [tex]\hat E\;=\;\frac{\hat x A\;+\;\hat y Be^{j\phi}}{\sqrt{A^2+B^2}}[/tex]

    Thanks
     
  2. jcsd
  3. Mar 12, 2013 #2
    That is correct. Any value of the imaginary exponential is on the unit circle in the complex plane, so its magnitude is unity.
     
  4. Mar 12, 2013 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    ##(Be^{j\phi})^2 = B^2e^{2j\phi}##, but what you want is ##|Be^{j\phi}|^2 = B^2##
     
  5. Mar 12, 2013 #4
    Thanks for the reply. So what you mean is:

    ##|\vec E|=\sqrt{A^2+|Be^{j\phi}|^2}##

    This is the main confusion for me. If you look at the ordinary way of finding the magnitude of a vector with real value, ##|\vec E|=\sqrt{(A)^2+(B)^2}##. So for complex vector we use "absolute" value......which means ##B^2=B\cdot B^*##?
     
  6. Mar 12, 2013 #5
    Thank you.
     
  7. Mar 12, 2013 #6
    The magnitude of complex vectors, just like that of real vectors, is defined via their inner (dot, scalar) product. Recall how the inner product of complex vectors is defined.
     
  8. Mar 12, 2013 #7
    Thank you very much. I see.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding unit vector
  1. Finding unit vectors (Replies: 3)

  2. Find the unit vector? (Replies: 3)

  3. Find a unit vector (Replies: 3)

  4. Finding a unit vector. (Replies: 2)

Loading...