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!

Properties of complex numbers

  1. Sep 18, 2009 #1
    Why is |z|^2 = z*z?

    z = a + ib
    z*z = (a - ib)(a + ib) = a^2 + b^2
    z^2 = (a + ib)^2 = a^2 + 2iab - b^2

    So it must have something to do with the absolute value, but I don't understand what or why.
  2. jcsd
  3. Sep 18, 2009 #2
    |z| does not define the "Absolute Value" of a complex number. The notation |z| refers to the modulus of z, which is by definition

    |z| = sqrt(a^2 + b^2)

    Geometrically it gives the distance of the complex number from the origin on the Argand Plane.

    And quite obviously |z|^2 is NOT EQUAL TO z^2
  4. Sep 18, 2009 #3


    User Avatar
    Science Advisor
    Homework Helper

    |z|^2 is conjugate(z)*z=a^2+b^2. It's not equal to z^2.
  5. Sep 19, 2009 #4
    although the modulus of z when z is of the form a + 0i (i.e. it is only in the reals), then wouldn't that be essentially like an absolute value?
  6. Sep 19, 2009 #5


    User Avatar
    Science Advisor
    Homework Helper

    Sure. Modulus of z is |z| is sqrt(a^2+b^2). It's still not the same as z^2. What's the question again?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Properties of complex numbers