Answer:
B (3 - i)
Step-by-step explanation:
To find the quotient of the complex numbers you must multiply the numerator and the denominator by the conjugate of the denominator
Example: The conjugate of (3 - i) is (3 + i)
[tex]\frac{8-6i}{3-i} *\frac{3+i}{3+i}[/tex]
[tex](3-i)(3+i)=9-i^{2}[/tex]
[tex]i^{2}=-1[/tex]
So [tex](3-i)(3+i)=9--1=10[/tex]
Denominator= 10
[tex](8-6i)(3+i)=24+8i-18i-6i^{2}[/tex]
[tex]24-10i-6i^{2} =24-10i-6(-1)=24-10i+6=30-10i[/tex]
Numerator = 30 - 10i
Then [tex]\frac{30-10i}{10} =\frac{30}{10}-\frac{10i}{10} = 3 - i[/tex]
The correct answer is B
