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

The solution to (3+i)/(2-3i) is 3/13+11/13 i

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

simplify

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

\frac{3}{13} + \frac{11}{13} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{( 3 + i ) ( 2 + 3 i )}{( 2 - 3 i ) ( 2 + 3 i )} : \frac{3 + 11 i}{13}

= \frac{3 + 11 i}{13}

Rewrite in standard complex form:

\frac{3}{13} + \frac{11}{13} i

= \frac{3}{13} + \frac{11}{13} i

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