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: Complex number argument and module

  1. Sep 21, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]z=\frac{(1-3i)^{100} * i * (7-5i)}{5+7i}[/tex]

    2. Relevant equations


    Find module and argument of z.

    3. The attempt at a solution

    Assuming:

    [tex]|z_1 * z_2| = |z_1||z_2|[/tex]

    [tex]|z|=\frac{|1-3i|^{100} * |i| * |7-5i|}{|5+7i|}[/tex]

    And now calculate each module individually by "Pythagoras theorems"

    [tex]|z|=\frac{\sqrt{10}^{100} * 1 *\sqrt{74}}{\sqrt{74}}=10^{50}[/tex]


    And I do now know how to calculate argument now.
     
    Last edited: Sep 21, 2010
  2. jcsd
  3. Sep 21, 2010 #2

    danago

    User Avatar
    Gold Member

    You could express each complex number in polar form and then simplify it using the properties of complex numbers expressed in polar form:

    [tex]\begin{array}{l}
    {r_1}cis({\theta _1}) \times {r_2}cis({\theta _2}) = {r_1}{r_2}cis({\theta _1} + {\theta _2})\\
    {\left( {rcis(\theta )} \right)^n} = {r^n}cis(n\theta )
    \end{array}[/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook