idiopatia0f

2022-01-16

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

Jimmy Macias

Beginner2022-01-17Added 30 answers

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

Beginner2022-01-18Added 43 answers

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.

$\Rightarrow \frac{3}{5i}=\frac{3}{5i}\times \frac{i}{i}=\frac{3i}{5{i}^{2}}$

Reminder${i}^{2}={\left(\sqrt{-1}\right)}^{2}=-1$

$\Rightarrow \frac{3i}{5{i}^{2}}=\frac{3i}{-5}=-\frac{3}{5}i$

This is achieved in this case by multiplying the numerator/denominator by i.

Reminder

alenahelenash

Skilled2022-01-24Added 366 answers