What is (1-4i)/(5+2i) ?

The solution to (1-4i)/(5+2i) is -3/29-22/29 i

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simplify (1-4i)/(5+2i)

simplify

\frac{1 - 4 i}{5 + 2 i}

- \frac{3}{29} - \frac{22}{29} i

Solution steps

\frac{1 - 4 i}{5 + 2 i}

Multiply by the conjugate

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

= \frac{( 1 - 4 i ) ( 5 - 2 i )}{( 5 + 2 i ) ( 5 - 2 i )}

Simplify

\frac{( 1 - 4 i ) ( 5 - 2 i )}{( 5 + 2 i ) ( 5 - 2 i )} : \frac{- 3 - 22 i}{29}

= \frac{- 3 - 22 i}{29}

Apply the fraction rule:

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

= \frac{- 3}{29} + \frac{- 22}{29} i

Simplify

\frac{- 3}{29} + \frac{- 22}{29} i : - \frac{3}{29} - \frac{22}{29} i

= - \frac{3}{29} - \frac{22}{29} i

- 18 \div 6

\frac{3}{5 + 2}

6 x - 3 x

5 x \cdot 3 x

\frac{\frac{x - 2}{2}}{\frac{x ^{2} - 4}{3}}