idiopatia0f

2022-01-16

How do you divide $\frac{3}{5i}$?

### Answer & Explanation

Jimmy Macias

Keep in mind that $i=\sqrt{-1}$ which means that ${i}^{2}=-1$ and therefore ${i}^{4}=1$. So we can rewrite the question as:
$\frac{3{i}^{4}}{5i}=\frac{3{i}^{3}}{5}$
${i}^{3}=-\sqrt{-1}=-i$ and so:
$\frac{3{i}^{4}}{5i}=\frac{3{i}^{3}}{5}=-\frac{3}{5}i$

Joseph Lewis

To divide this fraction we require the denominator to be a real number.
This is achieved in this case by multiplying the numerator/denominator by i.
$⇒\frac{3}{5i}=\frac{3}{5i}×\frac{i}{i}=\frac{3i}{5{i}^{2}}$
Reminder ${i}^{2}={\left(\sqrt{-1}\right)}^{2}=-1$
$⇒\frac{3i}{5{i}^{2}}=\frac{3i}{-5}=-\frac{3}{5}i$

alenahelenash

$\frac{3{i}^{4}}{5i}=\frac{3{i}^{3}}{5}$ ${i}^{3}=-\sqrt{-1}=-i$ $\frac{3{i}^{4}}{5i}=\frac{3{i}^{3}}{5}=-\frac{3}{5}i$