Given :
(4 - 3i)/(-1-4i)
We know that, i² = -1
Multiply the given complex number the conjugate of the denominator.
Now, we have
[tex]\frac{4-3i}{-1-4i} =\frac{4-3i}{-1-4i} * \frac{-1+4i}{-1+4i}\\ \\ = \frac{-4+16i+3i-12i^{2}}{1-4i+4i-16i^{2}} \\ \\ =\frac{8+19i}{17} [/tex]
∴ [tex]\frac{4-3i}{-1-4i} = \frac{8+19i}{17} = \frac{8}{17} + i \frac{19}{17}[/tex]
