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Math Help - complex numbers

  1. #1
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    complex numbers

    how do you solve

    (7+24i)/(x+iy)^2 = 1?

    i got x= 4i or x=-4i or x=3 or x=-3...
    but the answer is x =4, y=3 or x=-4, y=-3

    thanks!
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    how do you solve

    (7+24i)/(x+iy)^2 = 1?

    i got x= 4i or x=-4i or x=3 or x=-3...
    but the answer is x =4, y=3 or x=-4, y=-3

    thanks!
    7 + 24i = x^2 - y^2 + 2xy i.

    Therefore:

    7 = x^2 - y^2 .... (1)

    24 = 2xy .... (2)

    Solve simultaneously for x and y.
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  3. #3
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    Quote Originally Posted by alexandrabel90 View Post
    how do you solve

    (7+24i)/(x+iy)^2 = 1?

    i got x= 4i or x=-4i or x=3 or x=-3...
    but the answer is x =4, y=3 or x=-4, y=-3

    thanks!

    \frac{7+24i}{(x+iy)^2}=1 \Longrightarrow x^2-y^2+2xyi=7+24i

    Try to take it from here equating real and imaginary parts and choosing wisely the sign of solutions...

    Tonio
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