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Write as an imaginary number. Answer is j/12?

$\sqrt{- \frac{4}{16}}$ $sqrt(-4/16$

1 Answer

Dec 15, 2016

$\sqrt{- \frac{4}{16}} = \frac{i}{2}$ $sqrt(-4/16)=color(magenta)(i/2)$

Explanation:

$\sqrt{- \frac{4}{16}}$ $sqrt(-4/16)$
$XXX = \sqrt{- 1} \cdot \sqrt{\frac{4}{16}}$ $color(white)("XXX")=sqrt(-1) * sqrt(4/16)$

$XXX = \sqrt{- 1} \cdot \sqrt{\frac{1}{4}}$ $color(white)("XXX")=sqrt(-1) * sqrt(1/4)$

$XXX = \sqrt{- 1} \cdot \frac{\sqrt{1}}{\sqrt{4}}$ $color(white)("XXX")= sqrt(-1) * sqrt(1)/sqrt(4)$

$XXX = i \cdot \frac{1}{2} or \frac{1}{2} i or \frac{i}{2}$ $color(white)("XXX")= i * 1/2 or 1/2 i or i/2$

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I replaced your $j$ $j$ with an $i$ $i$ since from what I have observed here, $i$ $i$ is the more common symbol used here for $\sqrt{- 1}$ $sqrt(-1)$ (although I have seen $j$ $j$ used elsewhere).

I think the $1$ $1$ in your suggested answer $\frac{j}{12}$ $j/12$ was just a typo.

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