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

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

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

simplify

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

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

Solution steps

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

Rationalize

- \frac{2}{3 i + 1} : - \frac{( 1 + 3 i ) ( - 3 i + 1 )}{5}

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

(k^{2 m + n}) (k^{- 2 m - n})

6 x + 30

36 - 9 x^{2}

- \frac{25}{- 5}

x + x + 1

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