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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

- 2 + 4 i

Solution steps

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

Multiply by the conjugate

\frac{2 + i}{2 + i}

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

Simplify

\frac{( 1 - 3 i ) ( - 3 + i ) ( 2 + i )}{( 2 - i ) ( 2 + i )} : \frac{- 10 + 20 i}{5}

= \frac{- 10 + 20 i}{5}

Apply the fraction rule:

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

= \frac{- 10}{5} + \frac{20}{5} i

Simplify

\frac{- 10}{5} + \frac{20}{5} i : - 2 + 4 i

= - 2 + 4 i

(\frac{3 x ^{4}}{y})^{- 3}

3 (\frac{1}{3} a b^{2})^{3}

\frac{1 8 ^{2}}{z ^{3}}

3 h^{2} + 32 h + 20

(4 - i) (\frac{2}{5} - 2 i)