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Popular >

simplify 5/(3+i)

Solution

simplify

\frac{5}{3 + i}

Solution

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

Solution steps

\frac{5}{3 + i}

Multiply by the conjugate

\frac{3 - i}{3 - i}

= \frac{5 ( 3 - i )}{( 3 + i ) ( 3 - i )}

Simplify

\frac{5 ( 3 - i )}{( 3 + i ) ( 3 - i )} : \frac{15 - 5 i}{10}

= \frac{15 - 5 i}{10}

Apply the fraction rule:

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

= \frac{15}{10} + \frac{- 5}{10} i

Simplify

\frac{15}{10} + \frac{- 5}{10} i : \frac{3}{2} - \frac{1}{2} i

= \frac{3}{2} - \frac{1}{2} i

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Frequently Asked Questions (FAQ)

What is 5/(3+i) ?
The solution to 5/(3+i) is 3/2-1/2 i