What is (-2)/(1+sqrt(3)i) ?

The solution to (-2)/(1+sqrt(3)i) is -1/2+(sqrt(3))/2 i

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simplify (-2)/(1+sqrt(3)i)

simplify

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

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

Solution steps

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

Multiply by the conjugate

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

= \frac{- 2 ( 1 - 3 i )}{( 1 + 3 i ) ( 1 - 3 i )}

Simplify

\frac{- 2 ( 1 - 3 i )}{( 1 + 3 i ) ( 1 - 3 i )} : \frac{- 2 + 2 3 i}{4}

= \frac{- 2 + 2 3 i}{4}

Apply the fraction rule:

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

= \frac{- 2}{4} + \frac{2 3}{4} i

Simplify

\frac{- 2}{4} + \frac{2 3}{4} i : - \frac{1}{2} + \frac{3}{2} i

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

64 x^{8} y^{10}

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2 (x + 4) (x - 4)

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