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 Magnitude of complex number expression

  1. May 12, 2017 #1
    1. The problem statement, all variables and given/known data
    We are given Z, and are asked to find the magnitude of the expression. See attached picture(s)

    2. Relevant equations
    See attached pictures(s)

    3. The attempt at a solution
    When I solved it on the exam, I did it the long way using De Moivre's theorem. I ended up making a few sign errors which cost me points. When my professor went over the exam, he did the problem as shown on the second picture with the purple pen writing. What I am wondering is why you can solve it this way? Why in the denominator you can just multiple the magnitude of both terms without having to evaluate it? File_000.jpeg File_000 (1).jpeg
     
  2. jcsd
  3. May 13, 2017 #2

    Mark44

    Staff: Mentor

    Because, for example, ##|\frac z 2 | = \frac {|z|} 2##. The denominator in the original problem is a real number. The work done in just a few lines (in purple) is extension of my example. Being much simpler, it's the better approach.
     
  4. May 13, 2017 #3

    scottdave

    User Avatar
    Homework Helper
    Gold Member

    More generally, ##|\frac z w | = \frac {|z|} {|w|}##. For example, if z = |z|ei*argz and w = |w|ei*argw, then you can write z / w as (|z|/|w|)*ei*(argz-argw).Since ei*a has a magnitude of 1, then it has no effect on the magnitude.

    In general when you multiply two complex numbers, you multiply the magnitudes and add the angles. Dividing, you divide the magnitudes and subtract the angles.
     
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 Magnitude of complex number expression
Loading...