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Complex Analysis Properties Question

  1. Jun 16, 2015 #1

    RJLiberator

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    Use properties to show that:
    (question is in the attached picture)

    Now, it is my understanding that due to properties you can express (sqrt(5)-i) as the sqrt((sqrt(5))^2+(-1)^2) which equals sqrt(6).
    And (2zbar+5) can be represented as (2z+5).

    But this would be sqrt(6)*(2z+5) which is NOT sqrt(3)*(2z+5)

    Was there a typo in this problem? Or am I not thinking of something?

    Thank you.
     

    Attached Files:

  2. jcsd
  3. Jun 16, 2015 #2

    Dick

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    There are some absolute value signs missing, but yes, I think there is a typo.
     
  4. Jun 16, 2015 #3

    RJLiberator

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    Excellent. After performing the operations, I felt like I had a good understanding of it. This seems to confirm my suspicions :). Kind regards for your help tonight.
     
  5. Jun 17, 2015 #4

    Fredrik

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    What you wrote here is very far from true. The real number ##\sqrt{6}## obviously can't be equal to ##\sqrt{5}-i##, which isn't even real. But Dick said something about missing absolute value signs, so I suppose you could be talking about something like this: For all ##z,w\in\mathbb C##, if ##\operatorname{Re}\bar z w=0##, then ##|z+w|^2=|z|^2+|w|^2##. This implies that ##|\sqrt{5}-i|^2=|\sqrt{5}|^2+|-i|^2=5+1=6##, and this implies that ##\sqrt{6}=|\sqrt{5}-i|##.
     
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