Plasmataco
  • Plasmataco
what is the sqrt of i(imaginary)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Plasmataco
  • Plasmataco
\[\sqrt[4]{-1}\]
Plasmataco
  • Plasmataco
ppl... @jim_thompson5910 @dan815
Plasmataco
  • Plasmataco
@dan815 ? ur like the smartest guy ever so...

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Plasmataco
  • Plasmataco
tied for @jim_thompson5910
Plasmataco
  • Plasmataco
haaaaalp
jim_thompson5910
  • jim_thompson5910
so you're asking why this is true? \[\Large \sqrt{i} = \sqrt[4]{-1}\]
Plasmataco
  • Plasmataco
no, what does it equal.
Plasmataco
  • Plasmataco
is there like a different letter for that?
jim_thompson5910
  • jim_thompson5910
I just said it \(\LARGE \sqrt{i}\) is equal to \(\LARGE \sqrt[4]{-1}\)
Plasmataco
  • Plasmataco
but to reduce it without a radical sign.
jim_thompson5910
  • jim_thompson5910
\[\Large \sqrt{i} = \sqrt{\sqrt{-1}}\] \[\Large \sqrt{i} = \sqrt{(-1)^{1/2}}\] \[\Large \sqrt{i} = ((-1)^{1/2})^{1/2}\] \[\Large \sqrt{i} = (-1)^{1/2*1/2}\] \[\Large \sqrt{i} = (-1)^{1/4}\] \[\Large \sqrt{i} = \sqrt[4]{-1}\]
Plasmataco
  • Plasmataco
Im sry i might be asking the impossible.
jim_thompson5910
  • jim_thompson5910
You can either write it with a fractional exponent, or as a radical. I don't think it's possible to do it any other way
Plasmataco
  • Plasmataco
nvm
Plasmataco
  • Plasmataco
gtg tho bye
anonymous
  • anonymous
The answer to your question is \[\frac{1+i}{\sqrt 2}\]
Plasmataco
  • Plasmataco
oh. sry afk but thx!
IrishBoy123
  • IrishBoy123
\(\large \sqrt{i}=\frac{1+i}{\sqrt{2}}\) but why not also \(\large -\frac{1+i}{\sqrt{2}}\)?? \(\large\sqrt{e^{i \frac{\pi}{2} + 2n \pi}} = e^{i \frac{\pi}{4} + n \pi} = e^{i \frac{\pi}{4}}, e^{i \frac{5\pi}{4}}\) |dw:1442740104302:dw|
anonymous
  • anonymous
That's also true, of course. I was answering the question in the same way that one might say "The square root of nine is three". If we're being strict about it, the radical sign should not be used in this context because it only applies to positive, real numbers. It should be written something like \[ i^{1/2} =\left\{ \frac{(1+i)}{\sqrt{2}} , -\frac{1+i}{\sqrt{2}} \right\}\] \(\sqrt{i},\sqrt{-1}\), and other things like that don't actually make sense.
IrishBoy123
  • IrishBoy123
thank you

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