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

The solution to (1-4i)/(3+4i) is -13/25-16/25 i

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

simplify

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

- \frac{13}{25} - \frac{16}{25} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{( 1 - 4 i ) ( 3 - 4 i )}{( 3 + 4 i ) ( 3 - 4 i )} : \frac{- 13 - 16 i}{25}

= \frac{- 13 - 16 i}{25}

Apply the fraction rule:

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

= \frac{- 13}{25} + \frac{- 16}{25} i

Simplify

\frac{- 13}{25} + \frac{- 16}{25} i : - \frac{13}{25} - \frac{16}{25} i

= - \frac{13}{25} - \frac{16}{25} i

1 + (\frac{6}{5})^{2}

16 + 36

(- 8)^{\frac{1}{2}}

4 c + \frac{3 c}{1 + 0.08} = 220.37

\frac{1}{2} (6 x + 20) = x + 4 + 2 (x + 3)