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Homework Help: Complex number

  1. Apr 28, 2012 #1

    sharks

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    The problem statement, all variables and given/known data
    Given that the real and imaginary parts of the complex number [itex]z=x+iy[/itex] satisfy the equation [itex](2-i)x-(1+3i)y=7[/itex]. Find x and y.

    The attempt at a solution
    I know it's quite simple. Just equate the real and imaginary parts, but i checked and redid it again, but the answer still evades me!
    [tex](2x-y-7) + i(-x-3y)=0
    \\2x-y-7=x
    \\x-y=7\, (1)
    \\-x-3y=y
    \\4y+x=0\, (2)
    \\x=28/5
    \\y=-7/5
    [/tex]
    I replaced in the original equation but i can't get 7 on the L.H.S.
    The correct answers: x=3 and y=-1.
     
  2. jcsd
  3. Apr 28, 2012 #2

    LCKurtz

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    Why aren't those 0 on the right side?
     
  4. Apr 28, 2012 #3

    SammyS

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    When you write:
    [itex]2x-y-7=x[/itex]

    and

    [itex]-x-3y=y\ ,[/itex]​
    you are saying that
    [itex](2x-y-7) + i(-x-3y)=z\ .[/itex]​

    That's not what you're trying to solve !
     
  5. Apr 28, 2012 #4

    sharks

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    I was confused about z=x+iy. I thought i had to compare the real and imaginary parts of z with those of the equation in order to solve it. I now realize that it has absolutely nothing to do with z. All i had to do was solve the equation independently and ignore whatever was given for z.

    Solving:[tex]2x-y=7
    \\-x-3y=0[/tex]I get the correct answers.

    Thank you, LCKurtz and SammyS. :smile:
     
    Last edited: Apr 28, 2012
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