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

The solution to ((1+2i))/((3-4i)) is -1/5+2/5 i

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

simplify

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

- \frac{1}{5} + \frac{2}{5} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{( 1 + 2 i ) ( 3 + 4 i )}{( 3 - 4 i ) ( 3 + 4 i )} : \frac{- 5 + 10 i}{25}

= \frac{- 5 + 10 i}{25}

Apply the fraction rule:

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

= \frac{- 5}{25} + \frac{10}{25} i

Simplify

\frac{- 5}{25} + \frac{10}{25} i : - \frac{1}{5} + \frac{2}{5} i

= - \frac{1}{5} + \frac{2}{5} i

\frac{\frac{2}{3}}{\frac{1}{2}}

\frac{x ^{- 4}}{x ^{- 6}}

3 w^{2} + w - 1 = 0

1 + (- \frac{2}{3}) - (- \frac{9}{2})

3 x - 15 = 5 x - 23