# How do you write the following quotient in standard form (8+20i)/(2i)?

Sep 4, 2016

$\frac{8 + 20 i}{2 i} = 10 - 4 i$

#### Explanation:

We should remember that ${i}^{2} = - 1$ and hence we can simplify the given quotient by multiplying numerator and denominator by $i$. As such

$\frac{8 + 20 i}{2 i}$

= (i×(8+20i))/(i×2i)

= $\frac{8 i + 20 {i}^{2}}{2 {i}^{2}}$

= (8i+20×(-1))/(2×(-1))

= $\frac{- 20 + 8 i}{- 2}$

= $10 - 4 i$