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

The solution to 1/((1+3i)^2) is -2/25-3/50 i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

- \frac{2}{25} - \frac{3}{50} i

Solution steps

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

Expand

(1 + 3 i)^{2} : 6 i - 8

= \frac{1}{6 i - 8}

Rewrite

6 i - 8

in standard complex form:

- 8 + 6 i

= \frac{1}{- 8 + 6 i}

Multiply by the conjugate

\frac{- 8 - 6 i}{- 8 - 6 i}

= \frac{1 \cdot ( - 8 - 6 i )}{( - 8 + 6 i ) ( - 8 - 6 i )}

Simplify

\frac{1 \cdot ( - 8 - 6 i )}{( - 8 + 6 i ) ( - 8 - 6 i )} : \frac{- 8 - 6 i}{100}

= \frac{- 8 - 6 i}{100}

Apply the fraction rule:

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

= \frac{- 8}{100} + \frac{- 6}{100} i

Simplify

\frac{- 8}{100} + \frac{- 6}{100} i : - \frac{2}{25} - \frac{3}{50} i

= - \frac{2}{25} - \frac{3}{50} i

(\frac{2 x ^{3} y ^{2}}{3 x y})^{- 3}

\frac{1}{5} \cdot 25

3.64 + \frac{3}{5}

f (- 4) - g (2)