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

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

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

simplify

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

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

Solution steps

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

Rewrite

i - 3

in standard complex form:

- 3 + i

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

Multiply by the conjugate

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

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

Simplify

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

2 x^{3} + x^{2} - 23 x + 20

34 - 9

\frac{2}{4} + \frac{3}{10}

6 x^{2} + 17 x - 3

9 x + 2 + (3 x - 7) - 8 x

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