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iop360

find all complex numbers z such that z^2 = 7 - 24i give your answer in the form a+bi

  • one year ago
  • one year ago

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  1. iop360
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    |dw:1353792413116:dw|

    • one year ago
  2. myko
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    (a+bi)(a+bi)=7-24i a^2+2abi-b^2=7-24i now identify real and imaginary parts: a^2-b^2=7 2ab=-24 and solve this system for a and b

    • one year ago
  3. iop360
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    apparently im only supposed to get values of -4 and 4 for a...i get something different

    • one year ago
  4. iop360
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    because first i isolate for b = -12/a then i get 7 = (a-(12/a))(a+(12/a))

    • one year ago
  5. myko
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    a=-12/b substitute in 1º equation: 144/b^2-b^2=7 144/b^2=7+b^2 144=7b^2+b^4 new variable: b^2=x 144=7x+x^2 or x^2+7x-144=0 solve this

    • one year ago
  6. iop360
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    x = -16, 9

    • one year ago
  7. iop360
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    b^2 = -16 b^2 = 9 cant take b^2 = -16

    • one year ago
  8. iop360
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    so b = +/- 3

    • one year ago
  9. myko
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    right

    • one year ago
  10. myko
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    so: b^2=9 b=+-3

    • one year ago
  11. iop360
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    ok, i got it now...plug +/- 3 in equation

    • one year ago
  12. iop360
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    thanks!

    • one year ago
  13. myko
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    in a=-12/b

    • one year ago
  14. myko
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    yw

    • one year ago
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