Answer:
A. [tex]\frac{17}{25} -\frac{19}{25}i[/tex]
Step-by-step explanation:
To divide the complex number: [tex]\frac{5-i}{4+3i}[/tex], we rationalize with the conjugate of the denominator.
This gives us:
[tex]\frac{5-i}{4+3i} *\frac{4-3i}{4-3i}[/tex]
[tex]=\frac{(5-i)(4-3i)}{(4+3i)(4-3i)}[/tex]
We apply the distributive property to get:
[tex]\frac{20-15i-4i+3i^2}{4^2+3^2}[/tex]
We simplify to get:
[tex]\frac{20-19i+3(-1)}{(16+9)}[/tex]
This implies that:
[tex]\frac{20-19i-3}{(16+9)}[/tex]
[tex]\frac{17-19i}{25} =\frac{17}{25} -\frac{19i}{25}[/tex]
The correct answer is A.
