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Homework Help: Maxima, Minima complex function

  1. May 22, 2010 #1
    Hey

    my problem is that im unable to calculate the absolute value of the following function:

    [tex]f(z)=\bar{z}(z-2)-2\Re z[/tex] wherase [tex] z=x+iy [/tex]

    What i did was:

    [tex]=|z|^2-2\bar{z}-2\Re z=x^2+y^2-2x+2iy-2x=x^2+y^2+2yi-4x[/tex]

    and how should i calculate the absoulte value of this function??

    Because i should find all maxima and minima of |f(x)|, which is not so difficult, i hope after i got the abs()!

    Can anyone help me?
     
  2. jcsd
  3. May 22, 2010 #2

    gabbagabbahey

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    I don't think you are looking for the "absolute value", but rather the norm:

    [tex]|a+ib|=\sqrt{a^2+b^2}[/tex]
     
  4. May 22, 2010 #3
    yes, you're right, i mean the norm [tex]|a+ib|= \sqrt{a^2+b^2}[/tex] but how should i proceed?
     
  5. May 22, 2010 #4

    gabbagabbahey

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    Square the real and imaginary parts of your expression, add them together and take the square root of the result.
     
  6. May 22, 2010 #5
    you mean that:

    [tex]\abs(x^2+y^2-4x+2iy)=\sqrt{(x^2+y^2-4x)^2+4y^2}[/tex]

    that (x^2+y^2-4x) is the real part and 2iy the imaginary part?
     
  7. May 22, 2010 #6

    Mentallic

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    In [tex]a+ib[/tex], a is the real part and b is the imaginary part. That is, don't include the imaginary unit i in the imaginary part.

    And yes, you're right :smile:
     
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