Answer:
[tex]\frac{47}{37}[/tex] - [tex]\frac{14}{37}[/tex] i
Step-by-step explanation:
Given
[tex]\frac{8-i}{6+i}[/tex]
Multiply numerator/ denominator by the conjugate of the denominator.
The conjugate of 6 + i is 6 - i, thus
= [tex]\frac{(8-i)(6-i)}{(6+i)(6-i)}[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{48-14i+i^2}{36-i^2}[/tex] → substitute i² = - 1
= [tex]\frac{48-14i-1}{36+1}[/tex]
= [tex]\frac{47-14i}{37}[/tex]
= [tex]\frac{47}{37}[/tex] - [tex]\frac{14}{37}[/tex] i
