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{32}{- 8}

\frac{3}{x - 7} + \frac{x}{x - 7}

100 x^{2} y^{8} - 49 z^{4}

\frac{1}{5} \cdot (- 5)

\frac{1}{5 - 3 i} - \frac{1}{5 + 3 i}