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

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