What is ((15-8i)+(12-6i))/((-14+3i)-(-19-4i)) ?

The solution to ((15-8i)+(12-6i))/((-14+3i)-(-19-4i)) is 1/2-7/2 i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((15-8i)+(12-6i))/((-14+3i)-(-19-4i))

simplify

\frac{( 15 - 8 i ) + ( 12 - 6 i )}{( - 14 + 3 i ) - ( - 19 - 4 i )}

\frac{1}{2} - \frac{7}{2} i

Solution steps

\frac{( 15 - 8 i ) + ( 12 - 6 i )}{( - 14 + 3 i ) - ( - 19 - 4 i )}

Simplify

\frac{( 15 - 8 i ) + ( 12 - 6 i )}{( - 14 + 3 i ) - ( - 19 - 4 i )} : \frac{15 - 8 i + 12 - 6 i}{- 14 + 3 i - ( - 19 - 4 i )}

= \frac{15 - 8 i + 12 - 6 i}{- 14 + 3 i - ( - 19 - 4 i )}

Simplify

15 - 8 i + 12 - 6 i : - 14 i + 27

= \frac{- 14 i + 27}{- 14 + 3 i - ( - 19 - 4 i )}

Simplify

- 14 + 3 i - (- 19 - 4 i) : 7 i + 5

= \frac{- 14 i + 27}{7 i + 5}

Rewrite

- 14 i + 27

in standard complex form:

27 - 14 i

Rewrite

7 i + 5

in standard complex form:

5 + 7 i

= \frac{27 - 14 i}{5 + 7 i}

Multiply by the conjugate

\frac{5 - 7 i}{5 - 7 i}

= \frac{( 27 - 14 i ) ( 5 - 7 i )}{( 5 + 7 i ) ( 5 - 7 i )}

Simplify

\frac{( 27 - 14 i ) ( 5 - 7 i )}{( 5 + 7 i ) ( 5 - 7 i )} : \frac{37 - 259 i}{74}

= \frac{37 - 259 i}{74}

Apply the fraction rule:

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

= \frac{37}{74} + \frac{- 259}{74} i

Simplify

\frac{37}{74} + \frac{- 259}{74} i : \frac{1}{2} - \frac{7}{2} i

= \frac{1}{2} - \frac{7}{2} i

\frac{1}{4} x^{2} - 2 x + 3 \leq 0

0 = \frac{- 32}{81 ( x ^{2} - x - 20 )}

x^{2} + 7 x - 16 = 0

- \frac{1}{3} + \frac{1}{6}

What is ((15-8i)+(12-6i))/((-14+3i)-(-19-4i)) ?
The solution to ((15-8i)+(12-6i))/((-14+3i)-(-19-4i)) is 1/2-7/2 i