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Math Help - Complex Equations with a complex number and its conjugate

  1. #1
    Member alexgeek's Avatar
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    Question Complex Equations with a complex number and its conjugate

    Hi,
    I'm wondering how to solve equations such as the following:
     2z - \bar{z}i = 1+4i
    I tried replacing z with (x+yi) and \bar{x} with (x-yi) but that just gave me two unknowns.
    My textbook has something similar in one of the exercises but no examples for it.
    Thanks
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  2. #2
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by alexgeek View Post
    Hi,
    I'm wondering how to solve equations such as the following:
     2z - \bar{z}i = 1+4i
    I tried replacing z with (x+yi) and \bar{x} with (x-yi) but that just gave me two unknowns.
    My textbook has something similar in one of the exercises but no examples for it.
    Thanks
     2(x+iy) - (x-iy)i = 1 +4i

     2x+2yi - xi - y = 1 +4i

     (2x-y) +i(2y-x) = 1 +4i

    so complex numbers are equal if

     z_1 = x_1 + i y_1

     z_2 = x_2 + i y_2

     z_1 = z_2 \Rightarrow x_1 = x_2 \; \; and \; \;  y_1 = y_2

    so you have ...

     2x+y = 1

     2y-x = 4

    solve that (in any way that you know) and you will get your complex number Z = x+ iy







    solution :  x= -\frac {2}{5} \;\; y= \frac {9}{5}
    Last edited by yeKciM; September 13th 2010 at 10:22 AM.
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  3. #3
    Member alexgeek's Avatar
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    Ahh I got that far and didn't see it like that. Sort of like equating coefficients.
    Thanks
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  4. #4
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by alexgeek View Post
    Ahh I got that far and didn't see it like that. Sort of like equating coefficients.
    Thanks
    you're welcome
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