why is this true? \[\frac{2}{8i}=-\frac i 4\]

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why is this true? \[\frac{2}{8i}=-\frac i 4\]

Mathematics
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first off you can reduce, just like with real numbers then multiply top and bottom by \(i\)
because i*i=-1
or 1/i=-i

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Other answers:

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

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