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

Jan 30, 2016

$\frac{1}{10} - \frac{7}{10} i$

#### Explanation:

To ensure that the denominator is a real number multiply

numerator and denominator by the complex conjugate of

5 + 5i which is 5 - 5i

If a + bi is a complex number then conjugate is a - bi where a ,b

are real.

then (a + bi)( a - bl) $= {a}^{2} - a b i + a b i - {b}^{2} {i}^{2} = {a}^{2} + {b}^{2}$

which is real. (remembering that  i^2 = -1 )

hence $\frac{\left(4 - 3 i\right) \left(5 - 5 i\right)}{\left(5 + 5 i\right) \left(5 - 5 i\right)}$

distribute , using FOIL , to obtain

( 20 - 35i + 15i^2)/(25 - 25i^2)) =( 5 - 35i)/50

$= \frac{5}{50} - \frac{35}{50} i = \frac{1}{10} - \frac{7}{10} i$