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!

Homework Help: Properties of the modulus - complex variables question

  1. Sep 21, 2009 #1
    f(z) = (z+1) / (z-1) for z not equal to 1

    My teacher wrote
    |f(z)| = |x+1+iy| / |x-1+iy| = sqrt((x+1)^2 +1) / sqrt((x-1)^2 + 1)

    How do the values within the modulus work out to the right hand side? I can't figure it out.
  2. jcsd
  3. Sep 21, 2009 #2
    That's the definition of the modulus. You square the real part and then you square the imaginary part and add the two together and finally you take the square root. But I think there is an error since the imaginary part of z = x + iy is y, not 1.
  4. Sep 21, 2009 #3
    [tex]f(z) = \frac{z+1}{z-1}[/tex]

    [tex]|f(x+iy)| = \frac{|x+iy+1|}{|x+iy-1|}[/tex]

    [tex] = \frac{|x+1+iy|}{|x-1+iy|}[/tex]
    [tex] = \frac{\sqrt{(x+1)^2+(iy)^2}}{\sqrt{(x-1)^2+(iy)^2}}[/tex]
    [tex] = \frac{\sqrt{(x^2+2x+1)+(-y^2)}}{\sqrt{(x^2-2x+1)+(-y^2)}}[/tex]
    [tex] = \frac{\sqrt{(x^2+2x+1)+(-y^2)}}{\sqrt{(x^2-2x+1)+(-y^2)}}[/tex]

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