What is 4/(sqrt(3)-i) ?

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

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simplify 4/(sqrt(3)-i)

simplify

\frac{4}{3 - i}

3 + i

Solution steps

\frac{4}{3 - i}

Multiply by the conjugate

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

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

= 3 + i

\frac{\frac{1}{4}}{1}

(m + 2)^{3}

\frac{3}{10} \div \frac{6}{5}

\frac{8 x ^{2} y}{x ^{7} y ^{5}}

(2 a^{2} - a - 10) - (a^{2} + a + 13)