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Popular >

simplify 5/(1+3i)

Solution

simplify

\frac{5}{1 + 3 i}

Solution

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

Solution steps

\frac{5}{1 + 3 i}

Multiply by the conjugate

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

= \frac{5 ( 1 - 3 i )}{( 1 + 3 i ) ( 1 - 3 i )}

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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