What is 6/((-3i+1)^4) ?

The solution to 6/((-3i+1)^4) is 21/1250-36/625 i

Popular >

simplify 6/((-3i+1)^4)

simplify

\frac{6}{( - 3 i + 1 ) ^{4}}

\frac{21}{1250} - \frac{36}{625} i

Solution steps

\frac{6}{( - 3 i + 1 ) ^{4}}

Expand

(- 3 i + 1)^{4} : 96 i + 28

= \frac{6}{96 i + 28}

Rewrite

96 i + 28

in standard complex form:

28 + 96 i

= \frac{6}{28 + 96 i}

Multiply by the conjugate

\frac{28 - 96 i}{28 - 96 i}

= \frac{6 ( 28 - 96 i )}{( 28 + 96 i ) ( 28 - 96 i )}

Simplify

\frac{6 ( 28 - 96 i )}{( 28 + 96 i ) ( 28 - 96 i )} : \frac{168 - 576 i}{10000}

= \frac{168 - 576 i}{10000}

Apply the fraction rule:

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

= \frac{168}{10000} + \frac{- 576}{10000} i

Simplify

\frac{168}{10000} + \frac{- 576}{10000} i : \frac{21}{1250} - \frac{36}{625} i

= \frac{21}{1250} - \frac{36}{625} i

(1 - \frac{1}{4 z}) (1 - \frac{1}{2 z})

e^{2 x} (e^{x} x + e^{x} - 2 e^{- 2 x} C)

\frac{d}{d t} ((x) ((t^{2} + 5 t) (t - 10)))

π (\frac{125 - 21 21}{3} - 221)

- 2 a (2 sin (x) + x cos (x) + 2 b (2 cos (x) - x sin (x)))