Answer:
OPTION C
Step-by-step explanation:
To find the quotient of [tex]$ \frac{5 - 8i}{3 + 2i} $[/tex]
Multiplying and dividing by conjugate we get:
[tex]$ \frac{5 - 8i}{3 + 2i} \times \frac{3 - 2i}{3 - 2i} $[/tex]
[tex]$ = \frac{(5 - 8i)(3 - 2i)}{9 + 4} $[/tex]
[Since, [tex]$ (a + ib)(a - ib) = a^2 + b^2 $[/tex]]
[tex]$ = \frac{15 -10i -24i -16}{13} $[/tex]
[tex]$ \frac{-1 -34i}{13} $[/tex]
[tex]$ = \frac{-1}{13} - \frac{34i}{13} $[/tex]
Therefore, OPTION C is the answer.
