What is (3-2i)/(1+4i) ?

The solution to (3-2i)/(1+4i) is -5/17-14/17 i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (3-2i)/(1+4i)

simplify

\frac{3 - 2 i}{1 + 4 i}

- \frac{5}{17} - \frac{14}{17} i

Solution steps

\frac{3 - 2 i}{1 + 4 i}

Multiply by the conjugate

\frac{1 - 4 i}{1 - 4 i}

= \frac{( 3 - 2 i ) ( 1 - 4 i )}{( 1 + 4 i ) ( 1 - 4 i )}

Simplify

\frac{( 3 - 2 i ) ( 1 - 4 i )}{( 1 + 4 i ) ( 1 - 4 i )} : \frac{- 5 - 14 i}{17}

= \frac{- 5 - 14 i}{17}

Apply the fraction rule:

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

= \frac{- 5}{17} + \frac{- 14}{17} i

Simplify

\frac{- 5}{17} + \frac{- 14}{17} i : - \frac{5}{17} - \frac{14}{17} i

= - \frac{5}{17} - \frac{14}{17} i

\frac{225 π}{180}

\frac{( - 2 ) ^{4}}{( - 2 ) ^{2} + 2}

6 < 2 - 4 x < 8

12 x - 6 x^{2} = - 8

x^{2} y + x y^{2} + 2 x yz + x y^{2} + y^{3} + 2 y^{2} z