What is (1-4i)/(-3+2i) ?

The solution to (1-4i)/(-3+2i) is -11/13+10/13 i

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simplify (1-4i)/(-3+2i)

simplify

\frac{1 - 4 i}{- 3 + 2 i}

- \frac{11}{13} + \frac{10}{13} i

Solution steps

\frac{1 - 4 i}{- 3 + 2 i}

Multiply by the conjugate

\frac{- 3 - 2 i}{- 3 - 2 i}

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

Simplify

\frac{( 1 - 4 i ) ( - 3 - 2 i )}{( - 3 + 2 i ) ( - 3 - 2 i )} : \frac{- 11 + 10 i}{13}

= \frac{- 11 + 10 i}{13}

Rewrite in standard complex form:

- \frac{11}{13} + \frac{10}{13} i

= - \frac{11}{13} + \frac{10}{13} i

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\frac{x - 4}{x ^{2} - 5 x + 4}

\frac{( x + 1 )}{( x + 1 ) ^{2} + 1}