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

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

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

simplify

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

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

Solution steps

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

(1 + i) (1 - 2 i) (1 + 3 i) = 6 + 8 i

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

Multiply by the conjugate

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

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

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

- 2 (x - 1) - 12 < 2 (x + 1)

\frac{π}{4} - \frac{π}{8}

3 x - 4 + \frac{x}{4} < \frac{5 x}{2} + 2

9 x - 7 = - 7

- 4 x < 40

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