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iop360

  • 3 years ago

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

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  1. iop360
    • 3 years ago
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    |dw:1353792413116:dw|

  2. myko
    • 3 years ago
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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

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

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

  5. myko
    • 3 years ago
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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

  6. iop360
    • 3 years ago
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    x = -16, 9

  7. iop360
    • 3 years ago
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    b^2 = -16 b^2 = 9 cant take b^2 = -16

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

  9. myko
    • 3 years ago
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    right

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

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

  12. iop360
    • 3 years ago
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    thanks!

  13. myko
    • 3 years ago
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    in a=-12/b

  14. myko
    • 3 years ago
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    yw

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