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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


    [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


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    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:

    {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 )
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