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Popular >

simplify 5/(3i+1)

Solution

simplify

\frac{5}{3 i + 1}

Solution

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

Solution steps

\frac{5}{3 i + 1}

Rewrite

3 i + 1

in standard complex form:

1 + 3 i

= \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

Popular Examples

simplify 32^2 simplify

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4 x^{2} - 49 y^{2}

2 x + 4 < 12

(2x+1)/3+2x=(x-1)/4

\frac{2 x + 1}{3} + 2 x = \frac{x - 1}{4}

6 (- 7) - 18 = 180

Frequently Asked Questions (FAQ)

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