What is ((3-i))/(4+2i) ?

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

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simplify ((3-i))/(4+2i)

simplify

\frac{( 3 - i )}{4 + 2 i}

\frac{1}{2} - \frac{1}{2} i

Solution steps

\frac{3 - i}{4 + 2 i}

Multiply by the conjugate

\frac{4 - 2 i}{4 - 2 i}

= \frac{( 3 - i ) ( 4 - 2 i )}{( 4 + 2 i ) ( 4 - 2 i )}

Simplify

\frac{( 3 - i ) ( 4 - 2 i )}{( 4 + 2 i ) ( 4 - 2 i )} : \frac{10 - 10 i}{20}

= \frac{10 - 10 i}{20}

Apply the fraction rule:

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

= \frac{10}{20} + \frac{- 10}{20} i

Simplify

\frac{10}{20} + \frac{- 10}{20} i : \frac{1}{2} - \frac{1}{2} i

= \frac{1}{2} - \frac{1}{2} i

\frac{45}{24}

\frac{\frac{3}{2}}{( - \frac{\frac{2}{3}}{\frac{4}{12}} )}

2 (5 + 2)

7 \times \frac{1}{5}

- 3 x^{2} - 2 x^{2}