What is 4/(1+sqrt(3)i) ?

The solution to 4/(1+sqrt(3)i) is 1-sqrt(3)i

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simplify 4/(1+sqrt(3)i)

simplify

\frac{4}{1 + 3 i}

1 - 3 i

Solution steps

\frac{4}{1 + 3 i}

Multiply by the conjugate

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

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

= 1 - 3 i

(4 - r^{2})^{2}

3 a + 2 a

\frac{40 m ^{3} n ^{2} - 20 m ^{2} n ^{3}}{20 m ^{2} n ^{2}}

- 1^{12}

\frac{3}{8} \div \frac{5}{6}