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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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{12 d ^{10}}{3 ( d ^{- 4} ) ^{2}}

x^{4} - 3 x^{2} - 2 x

2 x^{2} - 12 x - 14

2 (x^{2} + 1)

(\frac{1}{2} - x)^{2}