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Homework Help: Complex Numbers

  1. Oct 7, 2007 #1
    [SOLVED] Complex Numbers

    1. The problem statement, all variables and given/known data

    I was given an equation with complex numbers, and told to convert to polar coordinates. I was able to find r relatively easily, but finding the angle is giving me trouble- I am having difficulties in breaking the equation down into imaginary and real parts.

    The equation:

    [tex]\frac{-6}{9+4i}[/tex]


    2. Relevant equations

    See part 1.



    3. The attempt at a solution

    I found r by doing the following:

    [tex]\frac{|-6|}{|9+4i|}[/tex]

    [tex]\frac{6}{\sqrt{81+16}}[/tex]

    [tex]r=\frac{6}{\sqrt{97}}[/tex]



    Now finding theta is where I get into trouble. I can't seem to understand what to do. I tried just doing it as if all of the fraction was imaginary, which would give me -pi/2 (am I right in thinking this?), but that doesn't work.
     
    Last edited: Oct 7, 2007
  2. jcsd
  3. Oct 7, 2007 #2

    ptr

    User Avatar

    Attempt to multiply the number by [tex]\frac{9-4i}{9-4i}[/tex]. Then you can easily separate the real and imaginary parts.
     
  4. Oct 7, 2007 #3

    Ahh wow thank you, I didn't even think of multiplying by the conjugate :approve:

    It's been years since I did complex numbers so I felt silly asking that, but thank you so much
     
  5. Oct 7, 2007 #4
    Did you get (6/Sqrt[97])e^(i*156º)?
     
    Last edited: Oct 7, 2007
  6. Oct 7, 2007 #5
    2.723368 radians :cool:
     
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