Given that
We have to divide the following
[tex]\frac{8-7i}{4-5i}[/tex]
Explanation -
Here we will use the rationalization method in which we will multiply and divide by the denominator by changing the sign in the denominator.
Also we will use the formula a^2 - b^2 = (a+b) (a-b)
In complex numbers i^2 = -1
Then,
[tex]\begin{gathered} \frac{8-7i}{4-5i}=\frac{8-7i}{4-5i}\times\frac{4+5i}{4+5i} \\ \\ \frac{8-7i}{4-5i}=\frac{(8-7i)(4+5i)}{(4-5i)(4+5i)}=\frac{32+40i-28i-35i^2}{16-(5i)^2} \\ \\ \frac{8-7i}{4-5i}=\frac{32+12i+35}{16+25}=\frac{67+12i}{41}=\frac{67}{41}+\frac{12}{41}i \end{gathered}[/tex]
So option D is correct.
Hence the final answer is 67/41 + 12i/41
