What is (5+i)/(1-3i) ?

The solution to (5+i)/(1-3i) is 1/5+8/5 i

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simplify (5+i)/(1-3i)

simplify

\frac{5 + i}{1 - 3 i}

\frac{1}{5} + \frac{8}{5} i

Solution steps

\frac{5 + i}{1 - 3 i}

Multiply by the conjugate

\frac{1 + 3 i}{1 + 3 i}

= \frac{( 5 + i ) ( 1 + 3 i )}{( 1 - 3 i ) ( 1 + 3 i )}

Simplify

\frac{( 5 + i ) ( 1 + 3 i )}{( 1 - 3 i ) ( 1 + 3 i )} : \frac{2 + 16 i}{10}

= \frac{2 + 16 i}{10}

Apply the fraction rule:

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

= \frac{2}{10} + \frac{16}{10} i

Simplify

\frac{2}{10} + \frac{16}{10} i : \frac{1}{5} + \frac{8}{5} i

= \frac{1}{5} + \frac{8}{5} i

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

5 x^{2} - 16 x - 16

∣ x + 4 ∣ = 2

4 - 4 i

2 x^{3} + x^{2} - 5 x + 2