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

The solution to (3+4i)/(4-2i) is 1/5+11/10 i

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

simplify

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

\frac{1}{5} + \frac{11}{10} i

Solution steps

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

Multiply by the conjugate

\frac{4 + 2 i}{4 + 2 i}

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

Simplify

\frac{( 3 + 4 i ) ( 4 + 2 i )}{( 4 - 2 i ) ( 4 + 2 i )} : \frac{4 + 22 i}{20}

= \frac{4 + 22 i}{20}

Apply the fraction rule:

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

= \frac{4}{20} + \frac{22}{20} i

Simplify

\frac{4}{20} + \frac{22}{20} i : \frac{1}{5} + \frac{11}{10} i

= \frac{1}{5} + \frac{11}{10} i

3 (72 - 32)

3 x + 2 < - 13

\frac{12 a ^{- 3} b ^{10}}{- 3 a ^{- 7} b ^{- 2}}

\frac{8 v}{28 w + 21} - \frac{3 v + 10}{4 w + 3}

5 + 2 x + x^{2} = 0