# How do you divide (-4+10i)/(3+4i)?

Aug 25, 2016

$\frac{- 4 + 10 i}{3 + 4 i} = \frac{28}{25} + \frac{46}{25} i$

#### Explanation:

To divide $- 4 + 10 i$ by $3 + 4 i$, one should multiply numerator and denominator by complex conjugate of denominator $3 + 4 i$ i.e. $3 - 4 i$. Also remember that ${i}^{2} = - 1$.

$\frac{- 4 + 10 i}{3 + 4 i}$

= ((-4+10i)×(3-4i))/((3+4i)×(3-4i))

= (-4)×3+(-4)(-4i)+10i×3+10i×((-4i))/(3×3+3×(-4i)+4i×3+4i×(-4i))

= $\frac{- 12 + 16 i + 30 i - 40 {i}^{2}}{9 - 12 i + 12 i - 16 {i}^{2}}$

= (-12+46i-40×(-1))/(9-16×(-1))

= $\frac{- 12 + 46 i + 40}{9 + 16}$

= $\frac{28 + 46 i}{25}$

= $\frac{28}{25} + \frac{46}{25} i$