Question

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Answer 1

Answer:

A. $\frac{17}{25} -\frac{19}{25}i$

Step-by-step explanation:

To divide the complex number: $\frac{5-i}{4+3i}$, we rationalize with the conjugate of the denominator.

This gives us:

$\frac{5-i}{4+3i} *\frac{4-3i}{4-3i}$

$=\frac{(5-i)(4-3i)}{(4+3i)(4-3i)}$

We apply the distributive property to get:

$\frac{20-15i-4i+3i^2}{4^2+3^2}$

We simplify to get:

$\frac{20-19i+3(-1)}{(16+9)}$

This implies that:

$\frac{20-19i-3}{(16+9)}$

$\frac{17-19i}{25} =\frac{17}{25} -\frac{19i}{25}$

The correct answer is A.