What is ((2+i))/((5+4i)) ?

The solution to ((2+i))/((5+4i)) is 14/41-3/41 i

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simplify ((2+i))/((5+4i))

simplify

\frac{( 2 + i )}{( 5 + 4 i )}

\frac{14}{41} - \frac{3}{41} i

Solution steps

\frac{2 + i}{5 + 4 i}

Multiply by the conjugate

\frac{5 - 4 i}{5 - 4 i}

= \frac{( 2 + i ) ( 5 - 4 i )}{( 5 + 4 i ) ( 5 - 4 i )}

Simplify

\frac{( 2 + i ) ( 5 - 4 i )}{( 5 + 4 i ) ( 5 - 4 i )} : \frac{14 - 3 i}{41}

= \frac{14 - 3 i}{41}

Rewrite in standard complex form:

\frac{14}{41} - \frac{3}{41} i

= \frac{14}{41} - \frac{3}{41} i

4 \times \frac{1}{6}

\frac{3}{7} + \frac{5}{2}

(2 y - 1) (y + 2)

6^{2} + 1 2^{2}

\frac{x - 8}{8 - x}