What is (3+4i)/(2+3i) ?

The solution to (3+4i)/(2+3i) is 18/13-1/13 i

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simplify (3+4i)/(2+3i)

simplify

\frac{3 + 4 i}{2 + 3 i}

\frac{18}{13} - \frac{1}{13} i

Solution steps

\frac{3 + 4 i}{2 + 3 i}

Multiply by the conjugate

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

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

Simplify

\frac{( 3 + 4 i ) ( 2 - 3 i )}{( 2 + 3 i ) ( 2 - 3 i )} : \frac{18 - i}{13}

= \frac{18 - i}{13}

Rewrite in standard complex form:

\frac{18}{13} - \frac{1}{13} i

= \frac{18}{13} - \frac{1}{13} i

21 6^{2}

22 \cdot 8

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