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Math Help - Quadratic and other polynomials

  1. #1
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    Exclamation Quadratic and other polynomials

    Please note: two complex numbers are equal when their real parts are equal and their imaginary parts are equal.
    i.e., if a+bi=c+di, then a=c and b=d


    Find real numbers X and Y for which:

    (X+yi)(y-i)=-4-7i
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  2. #2
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    Quote Originally Posted by Tessarina View Post
    Please note: two complex numbers are equal when their real parts are equal and their imaginary parts are equal.
    i.e., if a+bi=c+di, then a=c and b=d


    Find real numbers X and Y for which:

    (X+yi)(y-i)=-4-7i

    (x + yi)(y - i) = xy - xi + y^2i -i^2y

    xy + (y^2 - x)i + y

    y(x + 1) + (y^2 - x)i.


    The real parts need to be equal, and the imaginary parts need to be equal.

    So y(x + 1) = -4 and y^2 - x = -7.

    Solve these equations simultaneously for x and y.
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  3. #3
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    Quote Originally Posted by Tessarina View Post
    Please note: two complex numbers are equal when their real parts are equal and their imaginary parts are equal.
    i.e., if a+bi=c+di, then a=c and b=d


    Find real numbers X and Y for which:

    (X+yi)(y-i)=-4-7i
    Thanks for helping, but i tried to work it out and i still cant get it,

    This is the answer in the back of the book---
    X=-1
    Y=0
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  4. #4
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    Either you have copied the problem incorrectly or the answer is given incorrectly. If x= -1 and y= 0 then (x+yi)(y-i)= (-1+0i)(0- i)= (-1)(-i)= i, not -4- 7i.
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