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

The solution to (1+3i)/(2-i) is -1/5+7/5 i

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

simplify

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

- \frac{1}{5} + \frac{7}{5} i

Solution steps

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

Multiply by the conjugate

\frac{2 + i}{2 + i}

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

Simplify

\frac{( 1 + 3 i ) ( 2 + i )}{( 2 - i ) ( 2 + i )} : \frac{- 1 + 7 i}{5}

= \frac{- 1 + 7 i}{5}

Rewrite in standard complex form:

- \frac{1}{5} + \frac{7}{5} i

= - \frac{1}{5} + \frac{7}{5} i

\frac{5}{9} \cdot \frac{3}{5}

2 x^{2} - 11 x y - 21 y^{2}

3 a + 9 b + 7 a + 7

(- b^{3} c^{4})^{5}

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