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Popular >

simplify 4/(5+3i)

Solution

simplify

\frac{4}{5 + 3 i}

Solution

\frac{10}{17} - \frac{6}{17} i

Solution steps

\frac{4}{5 + 3 i}

Multiply by the conjugate

\frac{5 - 3 i}{5 - 3 i}

= \frac{4 ( 5 - 3 i )}{( 5 + 3 i ) ( 5 - 3 i )}

Simplify

\frac{4 ( 5 - 3 i )}{( 5 + 3 i ) ( 5 - 3 i )} : \frac{20 - 12 i}{34}

= \frac{20 - 12 i}{34}

Apply the fraction rule:

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

= \frac{20}{34} + \frac{- 12}{34} i

Simplify

\frac{20}{34} + \frac{- 12}{34} i : \frac{10}{17} - \frac{6}{17} i

= \frac{10}{17} - \frac{6}{17} i

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Frequently Asked Questions (FAQ)

What is 4/(5+3i) ?
The solution to 4/(5+3i) is 10/17-6/17 i