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Math Help - Proof using magnitude & conjugate properties (Complex Analysis)

  1. #1
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    Proof using magnitude & conjugate properties (Complex Analysis)

    (Hint: No need to change to x and y form)
    If , use the properties of magnitude, conjugate, etc. to prove:


    I'm just confused on where to start. I have all my notes on the properties on of magnitude and conjugate but I don't know how to apply them. Any hints on how to tackle this bad boy?
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  2. #2
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    Re: Proof using magnitude & conjugate properties (Complex Analysis)

    Quote Originally Posted by DrKittenPaws View Post
    (Hint: No need to change to x and y form)
    If , use the properties of magnitude, conjugate, etc. to prove:


    I'm just confused on where to start. I have all my notes on the properties on of magnitude and conjugate but I don't know how to apply them. Any hints on how to tackle this bad boy?
    you know that $\left|\frac{a}{b}\right|=\frac{|a|}{|b|}$ so just take the magnitudes top and bottom.

    $\left|az+b\right|=\left((az+b)( \overline{az+b}) \right)^{\frac{1}{2}}$

    do the same with the denominator and take the ratio.
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  3. #3
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    Re: Proof using magnitude & conjugate properties (Complex Analysis)

    Hi,
    As you suspected, it's just a matter of applying what you know about conjugates and absolute values. Here's a derivation:

    Proof using magnitude & conjugate properties (Complex Analysis)-mhfalgebra5.png
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  4. #4
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    Re: Proof using magnitude & conjugate properties (Complex Analysis)

    Quote Originally Posted by johng View Post
    Hi,
    As you suspected, it's just a matter of applying what you know about conjugates and absolute values. Here's a derivation:

    Click image for larger version. 

Name:	MHFalgebra5.png 
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    Thanks! I saw your answer too late but thankfully I did something similar. I did show your proof to a few of my classmates and they loved it. It was much more concise and clean than mine.
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