Question

How do you divide `(4-8i)/(6-5i)`?

Answer 1

=`64/51-(28i)/51`

Explanation:

To simplify a fraction in complex numbers, you must multiply the numerator and denominator by the conjugate of the denominator
In this case the conjugate is `6+5i`
`(4-8i)/(6-5i)=((4-8i)(6+5i))/((6-5i)(6+5i))=(24+20i-48i+40)/(51)=(64-28i)/51=64/51-(28i)/51`
`(6+5i)(6-5i)=36-25i^2=36+25=51` as `i^2=-1`