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Homework Help: Finding the angle without a calculator (CA)

  1. Mar 11, 2010 #1
    1. The problem statement, all variables and given/known data
    In my math class, we are not permitted to use a calculator. I am currently reviewing for a test and came across a small problem.

    Perform the following operation using the Euler (polar) form for the complex numbers involved.


    2. Relevant equations

    3. The attempt at a solution

    I know of 2 ways to write the numerator in polar form. Both depend on knowing the argument, or angle.

    1. (1-3i) = [tex]\sqrt{10}(cos{\theta}+i{sin{\theta}})[/tex]

    2. (1-3i)= [tex]\sqrt{10}e^{i\theta}[/tex]

    Performing the actual operation either in cartesian or Euler/polar form is not difficult for me. However I cannot think of how to find theta without a calculator.

    Is the 1, 3, [tex]\sqrt{10}[/tex] triangle a special triangle that I should have memorized?

    Like the 1, [tex]\sqrt{3}[/tex], 2 triangle with angle 60, or pi/3.
  2. jcsd
  3. Mar 11, 2010 #2


    Staff: Mentor

    The 1, 3, sqrt(10) triangle is NOT a special triangle that you are expected to have memorized. I wonder if there was a typo in your problem, and that maybe it should have been (1 - sqrt(3)i)/i.
  4. Mar 11, 2010 #3
    It could have been a typo. I spoke with a few upperclassman who have taken the course and they recommended to leave it implicitly.

    I guess tan^-1(3) will have to do. I'm going to speak with the professor before the exam. Thanks for confirming the memorization issue.
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