Complex numbers

  1. I just wanted to check something. If I have a complex number of the form

    [itex]a = C * \exp(i \phi) [/itex]

    where C is some non-complex scalar constant. Then the phase of this complex number is simply [itex]\phi[/itex]. Is that correct?
     
  2. jcsd
  3. jbunniii

    jbunniii 3,378
    Science Advisor
    Homework Helper
    Gold Member

    If ##C > 0## then this is almost correct. However, the phase is not well-defined under this definition, because ##C\exp(i\phi) = C\exp(i(\phi+2\pi n))## for any integer ##n##. You can get around this by defining the phase to be the coset ##\phi + 2\pi \mathbb{Z}## or by constraining it to be in the interval ##[0,2\pi)## or ##[-\pi, \pi)## or some other half-open interval of length ##2\pi##.

    If ##C < 0##, then you need to absorb the sign of ##C## into the phase:
    $$a = -|C|\exp(i \phi) = |C|\exp(i(\phi + \pi))$$

    If ##C = 0## then the phase is undefined.
     
    1 person likes this.
  4. Thank you for this detailed answer!
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?

0
Draft saved Draft deleted
Similar discussions for: Complex numbers
Loading...