anonymous
  • anonymous
Ignore this please...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
ignored
anonymous
  • anonymous
\[\frac{5}{\sqrt{-24}} = \frac{5}{2\sqrt{6}i} = \frac{5}{2\sqrt{6}i} \times \frac{0-2\sqrt{6}i}{0-2\sqrt{6}i}\]
anonymous
  • anonymous
oh ok

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anonymous
  • anonymous
Why 0 -?
anonymous
  • anonymous
\[\frac{5}{2\sqrt{6}i} \times \frac{0-2\sqrt{6}i}{0-2\sqrt{6}i} = \frac{-10\sqrt{6}i}{-24i^{2}}\]
anonymous
  • anonymous
Oh, so it can be postive.
anonymous
  • anonymous
0- because it's a complex conjugate
anonymous
  • anonymous
It's not needed, but I'm including it so you can see how it's a complex conjugate
anonymous
  • anonymous
ive never heard that term before
anonymous
  • anonymous
So any complex number can be written as\[(a+bi)\] The conjugate of that is \[(a-bi)\]The reason they're useful is because if you multiply them by each other, you get rid of the imaginary part:\[(a+bi) \times (a-bi) = a^{2} +abi -abi -b^{2}i^{2} = a^{2}+b^{2}\]
anonymous
  • anonymous
oh. i remember that. i dont think we ever did anything with it though so i forgot it
anonymous
  • anonymous
So if you have a term where you have an imaginary number in the denominator, you can "move" the imaginary number to the denominator by multiplying the fraction by the complex conjugate divided by itself (which equals 1)
anonymous
  • anonymous
Can you figure out the rest from there?
anonymous
  • anonymous
how did they get 2sqrt 6 in the denominator if you took the sqrt out?
anonymous
  • anonymous
If so, vote my answer as "Best Response"
anonymous
  • anonymous
It simplifies like this....
anonymous
  • anonymous
\[\frac{-10\sqrt{6}i}{-24i^{2}} = \frac{-5\times 6^{1/2}i}{(-12) \times (-1)}\]
anonymous
  • anonymous
\[\frac{-5\times 6^{1/2}i}{(-12) \times (-1)} = \frac{-5i}{2 \times 6^{1} \times 6^{-1/2}} = \frac{-5i}{2\times 6^{1/2}} = \frac{-5i}{2\sqrt{6}}\]
anonymous
  • anonymous
Does that make sense?
anonymous
  • anonymous
not really. im not used to seeing it done this way
anonymous
  • anonymous
how did it go from -24i to -12x-1? shouldnt it be 24 and -1?
anonymous
  • anonymous
The numerator reduced from 10 to 5 in that step. I canceled out a 2
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
So it was like \[\frac{(-1)(2)(5)\sqrt{6}i}{(-1)(2)(12)i^{2}}\] and I just canceled the 2's
anonymous
  • anonymous
yeah, i see that now. and you just dropped the 1/2 exponent to the bottom after?
anonymous
  • anonymous
Yeah, the sign of the exponent changes when you do that though.\[\frac{a^{b}}{1} = \frac{1}{a^{-b}}\]
anonymous
  • anonymous
ok i got it.

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