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

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

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

simplify

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

- 1 + 2 i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

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

= - 1 + 2 i

2 x^{2} - 2 x + 3 = 0

3 (4 k - \frac{1}{3}) = 12 k - 1

\frac{6}{10} \cdot \frac{4}{9}

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

\frac{9 !}{( 9 - 6 ) !}