# How do you divide (2+3i)/(4-5i)?

Jan 24, 2016

$- \frac{7}{41} + \frac{22}{41} i$

#### Explanation:

To divide the fraction : multiply the numerator and denominator

by the 'complex conjugate' of 4 - 5i which is 4 + 5i . This

changes the denominator to a real number.

 ((2 + 3i )(4 + 5i ))/((4 - 5i )(4 + 5i )

( distribute brackets using FOIL method )

$\frac{8 + 10 i + 12 i + 15 {i}^{2}}{16 + 20 i - 20 i - 25 {i}^{2}}$

(Note :  i^2 = - 1 )

$= \frac{8 + 22 i - 15}{16 + 25} = \frac{- 7 + 22 i}{16 + 25} = - \frac{7}{41} + \frac{22}{41} i$