Answer:
B
Step-by-step explanation:
Substitute x and y into the ratio, that is
[tex]\frac{x}{y}[/tex] = [tex]\frac{6-5i}{2+i}[/tex]
Rationalise the denominator by multiplying numerator/ denominator by
the complex conjugate of the denominator
The conjugate of 2 + i is 2 - i, thus
[tex]\frac{(6-5i)(2-i)}{(2+i)(2-i)}[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{12-16i+5i^2}{4-i^2}[/tex] ← note that i² = - 1
= [tex]\frac{12-16i-5}{4+1}[/tex]
= [tex]\frac{7-16i}{5}[/tex]
= [tex]\frac{7}{5}[/tex] - [tex]\frac{16}{5}[/tex] i ← in the form a + bi
with b = - [tex]\frac{16}{5}[/tex] → B
