anonymous
  • anonymous
find all complex numbers z such that z^2 = 7 - 24i give your answer in the form a+bi
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
(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
anonymous
  • anonymous
apparently im only supposed to get values of -4 and 4 for a...i get something different

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anonymous
  • anonymous
because first i isolate for b = -12/a then i get 7 = (a-(12/a))(a+(12/a))
anonymous
  • anonymous
a=-12/b substitute in 1ยบ 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
anonymous
  • anonymous
x = -16, 9
anonymous
  • anonymous
b^2 = -16 b^2 = 9 cant take b^2 = -16
anonymous
  • anonymous
so b = +/- 3
anonymous
  • anonymous
right
anonymous
  • anonymous
so: b^2=9 b=+-3
anonymous
  • anonymous
ok, i got it now...plug +/- 3 in equation
anonymous
  • anonymous
thanks!
anonymous
  • anonymous
in a=-12/b
anonymous
  • anonymous
yw

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