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

The solution to ((1+i)(1-2i))/(3+i) is 4/5-3/5 i

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

simplify

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

\frac{4}{5} - \frac{3}{5} i

Solution steps

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

Multiply by the conjugate

\frac{3 - i}{3 - i}

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

Simplify

\frac{( 1 + i ) ( 1 - 2 i ) ( 3 - i )}{( 3 + i ) ( 3 - i )} : \frac{8 - 6 i}{10}

= \frac{8 - 6 i}{10}

Apply the fraction rule:

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

= \frac{8}{10} + \frac{- 6}{10} i

Simplify

\frac{8}{10} + \frac{- 6}{10} i : \frac{4}{5} - \frac{3}{5} i

= \frac{4}{5} - \frac{3}{5} i

\frac{x - 1}{2} - 2 \leq \frac{3 x - 2}{5}

2 x^{4} + 13 x^{3} + 9 x^{2} - 40 x + 16 \geq 0

3 x - 1 > 5

\frac{1}{2} \cdot 2 π

\frac{1}{3} \cdot \frac{1}{6}