Respuesta :
Answer: The required simplified quotient is [tex]\dfrac{1}{10}-\dfrac{1}{5}i.[/tex]
Step-by-step explanation: We are given to find the following quotient :
[tex]Q=\dfrac{-2+i}{-8-6i}=\dfrac{2-i}{8+6i}.[/tex]
To find the given quotient, we must multiply both the numerator and denominator by the conjugate of (8+6i), that is, (8-6i).
So, we have
[tex]Q\\\\\\=\dfrac{2-i}{8+6i}\\\\\\=\dfrac{(2-i)(8-6i)}{(8+6i)(8-6i)}\\\\\\=\dfrac{16-12i-8i+6i^2}{64-36i^2}\\\\\\=\dfrac{16-20i-6}{64+36}~~~~~~~~~~~~~~~~~~[\textup{since }i^2=-1]\\\\\\=\dfrac{10-20i}{100}\\\\\\=\dfrac{1-2i}{10}\\\\\\=\dfrac{1}{10}-\dfrac{1}{5}i.[/tex]
Thus, the required simplified quotient is [tex]\dfrac{1}{10}-\dfrac{1}{5}i.[/tex]
