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

The solution to ((3-5i)^2)/(i(2+3i)) is -12/13+i 122/13

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

- \frac{12}{13} + i \frac{122}{13}

Solution steps

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

i (2 + 3 i) : - 3 + 2 i

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

(3 - 5 i)^{2} = - 16 - 30 i

= \frac{( - 16 - 30 i )}{- 3 + 2 i}

Apply complex arithmetic rule:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = - 16, b = - 30, c = - 3, d = 2

= \frac{( - 16 ( - 3 ) + ( - 30 ) \cdot 2 ) + ( - 30 ( - 3 ) - ( - 16 ) \cdot 2 ) i}{( - 3 ) ^{2} + 2 ^{2}}

Refine

= \frac{- 12 + 122 i}{13}

Rewrite

\frac{- 12 + 122 i}{13}

in standard complex form:

- \frac{12}{13} + \frac{122}{13} i

= - \frac{12}{13} + \frac{122}{13} i

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

- 8^{2}

(9 - 4 i)^{2}

\frac{2 x}{3 x ^{2}}

- (8 a - 0.2)

What is ((3-5i)^2)/(i(2+3i)) ?
The solution to ((3-5i)^2)/(i(2+3i)) is -12/13+i 122/13