Barrelracing
  • Barrelracing
Rationalize the denominator of square root of negative four over open parentheses 7 minus 3 i close parentheses plus open parentheses 2 plus 5 i.
Mathematics
jamiebookeater
  • jamiebookeater
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Barrelracing
  • Barrelracing
|dw:1437857496870:dw|
carolinar7
  • carolinar7
|dw:1437846970791:dw|
carolinar7
  • carolinar7
|dw:1437847013934:dw|

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anonymous
  • anonymous
|dw:1437846985513:dw|
carolinar7
  • carolinar7
No you need to multiply it by conjugate
carolinar7
  • carolinar7
Oh you did, my bad
anonymous
  • anonymous
the first thing you have to do is combine the denominator into one complex number. |dw:1437847204733:dw|
anonymous
  • anonymous
|dw:1437847105860:dw|
Barrelracing
  • Barrelracing
5 - 2i
anonymous
  • anonymous
that's (7 + 2) + (-3i + 5i)
Barrelracing
  • Barrelracing
9 +2
anonymous
  • anonymous
9 + 2i, so now you have \[\frac{ \sqrt{-4} }{ 9+2i }\]
anonymous
  • anonymous
can you write √-4 in terms of i?
Barrelracing
  • Barrelracing
no
anonymous
  • anonymous
\[\sqrt{-4}=\sqrt{4} \times \sqrt{-1}=2i\]
anonymous
  • anonymous
^do you understand that?
anonymous
  • anonymous
so now we have \[\frac{ 2i }{ 9+2i }\]
anonymous
  • anonymous
and now you can multiply by the conjugate like @carolinar7 said above
Barrelracing
  • Barrelracing
ok I don't know how to do that
anonymous
  • anonymous
to find the conjugate change the sign of the imaginary part of the denominator. → 9-2i Then multiply the numerator and denominator by it. \[\frac{ 2i(9-2i) }{ (9+2i)(9-2i) }\] Distribute/foil and the i's will cancel in the denominator
Barrelracing
  • Barrelracing
18i - 4/77
Barrelracing
  • Barrelracing
-4+18i/77
anonymous
  • anonymous
You had this at some point \[\frac{ 18i-4i^2 }{ 81-4i^2 }\] Remember that i² = -1, so you'll have \[\frac{ 4+18i }{ 85 }\]
Barrelracing
  • Barrelracing
thank you
anonymous
  • anonymous
you're welcome

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