Question

Find the quotient of these complex numbers.(8 - 7i) (4 - 5i) =

Answer 1

Given that

We have to divide the following

$\frac{8-7i}{4-5i}$

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,

$\begin{gathered} \frac{8-7i}{4-5i}=\frac{8-7i}{4-5i}\times\frac{4+5i}{4+5i} \\ \\ \frac{8-7i}{4-5i}=\frac{(8-7i)(4+5i)}{(4-5i)(4+5i)}=\frac{32+40i-28i-35i^2}{16-(5i)^2} \\ \\ \frac{8-7i}{4-5i}=\frac{32+12i+35}{16+25}=\frac{67+12i}{41}=\frac{67}{41}+\frac{12}{41}i \end{gathered}$

So option D is correct.

Hence the final answer is 67/41 + 12i/41