anonymous
  • anonymous
why is this true? \[\frac{2}{8i}=-\frac i 4\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
first off you can reduce, just like with real numbers then multiply top and bottom by \(i\)
anonymous
  • anonymous
because i*i=-1
anonymous
  • anonymous
or 1/i=-i

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anonymous
  • anonymous
Is our goal to get the imaginary number out of the denominator?
anonymous
  • anonymous
|dw:1358398893659:dw|
anonymous
  • anonymous
\[\frac{2}{8i}=\frac{1}{4i}=\frac{1}{4i}\times \frac{i}{i}=\frac{i}{4i^2}=-\frac{i}{4}\]
anonymous
  • anonymous
What is wrong if I say 1/i=i
anonymous
  • anonymous
it is \(\frac{1}{i}=-i\)
anonymous
  • anonymous
@sauravshakya you cannot use \(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\) unless \(a\) and \(b\) are real
anonymous
  • anonymous
ya I got how u got 1/i=-i But |dw:1358399037098:dw| this doesn't work
anonymous
  • anonymous
no it does not
anonymous
  • anonymous
1 and -1 are real
anonymous
  • anonymous
even this doesn't work \[\sqrt{a}\sqrt{b}=\sqrt{ab}\] unless \(a\) and \(b\) are positive numbers
anonymous
  • anonymous
excuse me i said 'real' and i meant 'positive' my mistake
anonymous
  • anonymous
oh I got it...
anonymous
  • anonymous
@JenniferSmart1 yes the goal is to get the complex number out of the denominator to write in standard form \(a+bi\)
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
make sense
anonymous
  • anonymous
so i*i=-1?
anonymous
  • anonymous
I'm too tired...I'll look at it again tomorrow. Thanks guys

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