Answer:
B
Step-by-step explanation:
To divide the fraction, multiply the numerator and denominator by the complex conjugate of the denominator.
The conjugate of 2 - 3i is 2 + 3i, thus
= [tex]\frac{(3+i)(2+3i)}{(2-3i)(2+3i)}[/tex]
Expand numerator/ denominator using FOIL
= [tex]\frac{6+11i+3i^2}{4-9i^2}[/tex] → note i² = - 1
= [tex]\frac{6+11i-3}{4+9}[/tex]
= [tex]\frac{3+11i}{13}[/tex]
= [tex]\frac{3}{13}[/tex] + [tex]\frac{11}{13}[/tex] i → B
