What is ((10-4i))/((5+i)) ?

The solution to ((10-4i))/((5+i)) is 23/13-15/13 i

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simplify ((10-4i))/((5+i))

simplify

\frac{( 10 - 4 i )}{( 5 + i )}

\frac{23}{13} - \frac{15}{13} i

Solution steps

\frac{10 - 4 i}{5 + i}

Multiply by the conjugate

\frac{5 - i}{5 - i}

= \frac{( 10 - 4 i ) ( 5 - i )}{( 5 + i ) ( 5 - i )}

Simplify

\frac{( 10 - 4 i ) ( 5 - i )}{( 5 + i ) ( 5 - i )} : \frac{46 - 30 i}{26}

= \frac{46 - 30 i}{26}

Apply the fraction rule:

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

= \frac{46}{26} + \frac{- 30}{26} i

Simplify

\frac{46}{26} + \frac{- 30}{26} i : \frac{23}{13} - \frac{15}{13} i

= \frac{23}{13} - \frac{15}{13} i

(2 x^{2}) - (- 4 x^{2} + x)

\frac{10}{64}

2 (6 x + 4) + 7 x

(4 - 3 m) 8

2 (2 + 1)^{2}