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How do i find the principal form of this complex number

  1. Dec 14, 2012 #1
    z= (10-j+elogj)2


    I tried expanding but it just made it more complicated.
    help please!!
     
  2. jcsd
  3. Dec 14, 2012 #2
    the principal form is defined in my book as
    ln(z)=ln(r)+jθ
     
  4. Dec 14, 2012 #3

    I like Serena

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    Hi iampaul!

    To find the principal form you need to find the length and the angle of z.
    First step is to find the length and angle of 10-j.
    And also of elogj.
    Do you know how?
     
  5. Dec 15, 2012 #4
    How?
    That's exactly what my problem is.
    10-j and elogj
    aren't similar to any of the forms discussed in school.
    Can you give another hint?
     
  6. Dec 15, 2012 #5

    I like Serena

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    Let's try and find ln(z)=ln(r)+jθ for 10-j and for elogj.

    ln(10-j) = -j ln(10) = ln(1) - j ln(10)

    So what is the length r and what is the angle θ for 10-j?


    Let's break elogj apart a little further.

    First we look at "j".
    Did you know that "j" has length 1 and angle pi/2?
    In other words, we have:
    $$j = e^{j {\pi \over 2}}$$

    Can you take the log of j?

    And if so, find the length and angle of elogj?
     
  7. Dec 17, 2012 #6
    thanks!!
     
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