When dividing complex numbers, we multiplicate both numerator and denominator by the conjugate of the denominator, like this:
Let:
z' = 1 - 4i (conjugate)
So:
[tex] \frac{3 - 2i}{1 + 4i} . \frac{1 - 4i}{1 - 4i} [/tex]
[tex] \frac{3 - 12i - 2i + 8i^2}{1 - 4i + 4i - 16i^2} [/tex]
[tex] \frac{3 - 14i + 8( \sqrt{-1})^2 }{1 - 16( \sqrt{-1})^2 } [/tex]
[tex] \frac{3 - 14i + 8(-1)}{1 - 16(-1)} [/tex]
[tex] \frac{3 - 14i - 8}{1 + 16} [/tex]
[tex] \frac{- 5 - 14i}{17} [/tex]
It's done, all steps have been made.
Hope it helps.
