Write each quotient as a complex number. \frac{4-3i}{-1-4i}

Write each quotient as a complex number
${\displaystyle \frac{4-3i}{-1-4i}}$
Key concept: you can use complex conjugates to simplify quotients of complex numbers.
${\displaystyle \frac{4-3i}{-1-4i}\cdot (-1+4i)}$
Rewrite the quotient so you are able to distribute
${\displaystyle \frac{(-1+4i)(4-3i)}{(-1+4i)(-1-4i)}}$
Distribute
${\displaystyle \frac{-4+3i+16i-12i^2}{1+4i-4i-{16}^2}}$
Key Concept: ${\displaystyle i^2-1}$
${\displaystyle \frac{-4+3i+16i-12(-1)}{1+4i-4i-16(-1)}}$
Simplify the equation
${\displaystyle \frac{8+19i}{17}}$
Simplify so the real part is apart from the imaginary part
${\displaystyle \frac{8}{17}+\frac{19i}{17}}$
Result:
${\displaystyle \frac{8}{17}+\frac{19i}{17}}$