anonymous
  • anonymous
write (square root) of -32 in simplified complex form
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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zepdrix
  • zepdrix
Hey there :) Here is a clever way that we can break up the negative sign and the 32.\[\large\rm \sqrt{-32}\quad=\sqrt{-1\cdot 32}\quad=\sqrt{-1}\cdot\sqrt{32}\]
zepdrix
  • zepdrix
Recall that we define our `imaginary unit` in this way: \(\large\rm \color{orangered}{\sqrt{-1}=i}\)
zepdrix
  • zepdrix
Do you understand how that is going to help us?\[\large\rm \color{orangered}{\sqrt{-1}}\cdot\sqrt{32}\quad=\quad ?\]

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anonymous
  • anonymous
yes
zepdrix
  • zepdrix
\[\large\rm \color{orangered}{\sqrt{-1}}\cdot\sqrt{32}\quad=\color{orangered}{i}\cdot\sqrt{32}\]Good, we can input our imaginary unit, ya? Another good step we can apply, is to pull anything out the root if we can.
zepdrix
  • zepdrix
So does the value 32 contain any `factors` that are perfect squares? These are perfect squares: 4, 9, 16, 25, 36, ... Does 32 have any of those values as factors?
anonymous
  • anonymous
ya 16 and 2
zepdrix
  • zepdrix
Ok great, let's apply that earlier trick again,\[\large\rm i\cdot \sqrt{32}\quad=i\cdot \sqrt{16\cdot2}\quad=i\cdot \sqrt{16}\cdot\sqrt{2}\]
zepdrix
  • zepdrix
And then what's the last simplification step you can do? :)
zepdrix
  • zepdrix
See it?
anonymous
  • anonymous
square root 16
anonymous
  • anonymous
i|dw:1450052445182:dw|
anonymous
  • anonymous
thats what i got as the answer
zepdrix
  • zepdrix
Nice! Good job! :)
anonymous
  • anonymous
k ty ty ty medal 4 u

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