What is (4+i)/(2+9i) ?

The solution to (4+i)/(2+9i) is 1/5-2/5 i

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simplify (4+i)/(2+9i)

simplify

\frac{4 + i}{2 + 9 i}

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

Solution steps

\frac{4 + i}{2 + 9 i}

Multiply by the conjugate

\frac{2 - 9 i}{2 - 9 i}

= \frac{( 4 + i ) ( 2 - 9 i )}{( 2 + 9 i ) ( 2 - 9 i )}

Simplify

\frac{( 4 + i ) ( 2 - 9 i )}{( 2 + 9 i ) ( 2 - 9 i )} : \frac{17 - 34 i}{85}

= \frac{17 - 34 i}{85}

Apply the fraction rule:

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

= \frac{17}{85} + \frac{- 34}{85} i

Simplify

\frac{17}{85} + \frac{- 34}{85} i : \frac{1}{5} - \frac{2}{5} i

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

1 + \frac{x ^{2}}{4 - x ^{2}}

\frac{7 - 6 i}{7 + i}

lo g_{8} (- 1)

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

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