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

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

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

simplify

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

- \frac{1}{10} - \frac{13}{10} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

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

= \frac{- 1 - 13 i}{10}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{- 1}{10} + \frac{- 13}{10} i

Simplify

\frac{- 1}{10} + \frac{- 13}{10} i : - \frac{1}{10} - \frac{13}{10} i

= - \frac{1}{10} - \frac{13}{10} i

2 \cdot 1 0^{4} - 7^{3}

y^{2} + 5 y - 6

\frac{- 18}{- 9}

(8 w^{2} z^{- 2})^{2} (z^{3})

\frac{60}{75}