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

\frac{- 2. 9 ^{3} + 27}{- 2.9 + 3}

(4 y + 7)^{2}

- 2 (9 + 2 a) - 8 (4 - 5 a)

(1 - x) (2 - x) (1 - x)