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Verified Answer :

FGX516

When dividing complex numbers, we multiplicate both numerator and denominator by the conjugate of the denominator, like this:

Let:

z' = 1 - 4i (conjugate)

So:

\(\frac{3 - 2i}{1 + 4i} . \frac{1 - 4i}{1 - 4i}\)

\(\frac{3 - 12i - 2i + 8i^2}{1 - 4i + 4i - 16i^2}\)

\(\frac{3 - 14i + 8( \sqrt{-1})^2 }{1 - 16( \sqrt{-1})^2 }\)

\(\frac{3 - 14i + 8(-1)}{1 - 16(-1)}\)

\(\frac{3 - 14i - 8}{1 + 16}\)

\(\frac{- 5 - 14i}{17}\)

It's done, all steps have been made.

Hope it helps.

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