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Popular >

simplify 4/(5+i)

Solution

simplify

\frac{4}{5 + i}

Solution

\frac{10}{13} - \frac{2}{13} i

Solution steps

\frac{4}{5 + i}

Multiply by the conjugate

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

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

Simplify

\frac{4 ( 5 - i )}{( 5 + i ) ( 5 - i )} : \frac{20 - 4 i}{26}

= \frac{20 - 4 i}{26}

Apply the fraction rule:

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

= \frac{20}{26} + \frac{- 4}{26} i

Simplify

\frac{20}{26} + \frac{- 4}{26} i : \frac{10}{13} - \frac{2}{13} i

= \frac{10}{13} - \frac{2}{13} i

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Frequently Asked Questions (FAQ)

What is 4/(5+i) ?
The solution to 4/(5+i) is 10/13-2/13 i