Dividing complex numbers formula:
[tex]\begin{gathered} \frac{a+bi}{c+di}=\frac{a+bi}{c+di}\times\frac{c-di}{c-di} \\ \\ =\frac{ac+bd}{c^2+d^2}+\frac{bc-ad}{c^2+d^2}i \end{gathered}[/tex]
For the given division:
[tex]\begin{gathered} \frac{8-7i}{4-5i}=\frac{8*4+(-7*-5)}{4^2+(-5)^2}+\frac{-7*4-(8*-5)}{4^2+(-5)^2}i \\ \\ =\frac{32+35}{16+25}+\frac{-28+40}{16+25}i \\ \\ =\frac{67}{41}+\frac{12}{41}i \end{gathered}[/tex]Answer: C
