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Finding X, Y in complex numbers.

  1. May 28, 2014 #1
    1. The problem statement, all variables and given/known data

    8i = ( 2x + i ) (2y + i ) + 1

    The final answers is [x =0, 4]
    [y=4, 0]

    2. Relevant equations



    3. The attempt at a solution

    The final answer in the book is stated as above but if I follow the solution I will get the real parts which would
    Equal 0=4xy meaning that both x and y when solving for either wil equal zero. If I continue the result I will get is

    [X= 0, Y= 4]

    I get one solution instead of 2 as provided in the book..
     
  2. jcsd
  3. May 28, 2014 #2

    rude man

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    x=0 and y=4 is indeed one solution. There is another one and it's very similar to the first. Hint: note the symmetry of the real and imaginary equations in terms of x and y!
     
  4. May 28, 2014 #3
    I don't see your attempt at a solution...?
    If you are given number = a *b +another number, then it is obvious that number - another number = a*b
    In the case of complex numbers, if we call the Real part of x, Re(x), and Im(x) for the imaginary part so that x = Re(x)+Im(x), then it is straightforward that:
    Re(number-another number) = Re((2x+i)(2y+i)) and
    Im(number-another number) = Im((2x+i)(2y+i)) and
    this gives you two equations and two unknowns.
     
  5. May 28, 2014 #4

    rude man

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    OK, how did you arrive at x=0, y=4? (Your post 1). Show every step.
     
    Last edited: May 29, 2014
  6. May 29, 2014 #5

    rude man

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    x and y are real numbers.
     
  7. May 29, 2014 #6
    My answers X=0 and Y=4 were correct, I talked to the teacher and he said the final answers given were wrong

    Here's how I came up with it:

    8i = 4xy + 2xi + 2yi + i^2 + 1

    0 + 8i = 4xy + 2xi + 2yi -1 + 1 [ Since i^2 equals -1 ]

    Real part = real part thus

    0=4xy

    X = 0/4y

    X=0

    Imaginary part = imaginary part thus

    8 =2x + 2y

    -2y = 2x -8

    2y = 8-2x

    Y = (8-2x)/2.. Now substitute with X=0

    Y = (8-0)/2

    Y= 4

    [ X= 0, Y=4]


    This is the correct solution. Thanks for the help everyone ^^
     
  8. May 29, 2014 #7

    LCKurtz

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    ##4xy=0## means either ##x=0## or ##y=0##. You only have one of the two answers.

    It is an incomplete solution. ##x=4,~y=0## also works as suggested in post #2.
     
  9. May 30, 2014 #8

    rude man

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    Looks like LC did the rest for you. It is correct. If your teacher said the two answers are wrong then HE is wrong.
     
  10. May 30, 2014 #9
    I also did that when I didn't get the answer same as mine but I think the difference is that X doesn't equal 0 and 4 in the same formation; X either equals 0 or 4 depends on what you solve for.. It doesn't equal 0 and 4 when we solve for the same variant such as

    x (x-4)=0

    Where X will equal both 0 and 4 and get final answer as [x = 0, 4] instead of [x =0] only or [x=4] only.. I talked to the teacher about the possibility of when X equals 0
    When we solve for x at 4xy = 0 and when it equals 4 when we solve for Y at the same part and he said they're both correct.8
     
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