What is (8+i)/(12-4i) ?

The solution to (8+i)/(12-4i) is 23/40+11/40 i

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simplify (8+i)/(12-4i)

simplify

\frac{8 + i}{12 - 4 i}

\frac{23}{40} + \frac{11}{40} i

Solution steps

\frac{8 + i}{12 - 4 i}

Multiply by the conjugate

\frac{12 + 4 i}{12 + 4 i}

= \frac{( 8 + i ) ( 12 + 4 i )}{( 12 - 4 i ) ( 12 + 4 i )}

Simplify

\frac{( 8 + i ) ( 12 + 4 i )}{( 12 - 4 i ) ( 12 + 4 i )} : \frac{92 + 44 i}{160}

= \frac{92 + 44 i}{160}

Apply the fraction rule:

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

= \frac{92}{160} + \frac{44}{160} i

Simplify

\frac{92}{160} + \frac{44}{160} i : \frac{23}{40} + \frac{11}{40} i

= \frac{23}{40} + \frac{11}{40} i

2 a + 6 a - 7 a

22 \frac{1}{2}

6 qw + 6 w - 3 wq - q

121 - 21

2 \times 3 x^{2}