What is (5-2i)/(7+3i) ?

The solution to (5-2i)/(7+3i) is 1/2-1/2 i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (5-2i)/(7+3i)

simplify

\frac{5 - 2 i}{7 + 3 i}

\frac{1}{2} - \frac{1}{2} i

Solution steps

\frac{5 - 2 i}{7 + 3 i}

Multiply by the conjugate

\frac{7 - 3 i}{7 - 3 i}

= \frac{( 5 - 2 i ) ( 7 - 3 i )}{( 7 + 3 i ) ( 7 - 3 i )}

Simplify

\frac{( 5 - 2 i ) ( 7 - 3 i )}{( 7 + 3 i ) ( 7 - 3 i )} : \frac{29 - 29 i}{58}

= \frac{29 - 29 i}{58}

Apply the fraction rule:

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

= \frac{29}{58} + \frac{- 29}{58} i

Simplify

\frac{29}{58} + \frac{- 29}{58} i : \frac{1}{2} - \frac{1}{2} i

= \frac{1}{2} - \frac{1}{2} i

(- 0.6 m^{3} n^{2})^{3}

\frac{800}{3}

\frac{2}{x - 2} + \frac{x}{x + 9} - \frac{x + 20}{x ^{2} + 7 x - 18}

- 2 x + 6 x - 11 x

245 a b^{5}