What is (2+3i)/(5-4i) ?

The solution to (2+3i)/(5-4i) is -2/41+23/41 i

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simplify (2+3i)/(5-4i)

simplify

\frac{2 + 3 i}{5 - 4 i}

- \frac{2}{41} + \frac{23}{41} i

Solution steps

\frac{2 + 3 i}{5 - 4 i}

Multiply by the conjugate

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

= \frac{( 2 + 3 i ) ( 5 + 4 i )}{( 5 - 4 i ) ( 5 + 4 i )}

Simplify

\frac{( 2 + 3 i ) ( 5 + 4 i )}{( 5 - 4 i ) ( 5 + 4 i )} : \frac{- 2 + 23 i}{41}

= \frac{- 2 + 23 i}{41}

Rewrite in standard complex form:

- \frac{2}{41} + \frac{23}{41} i

= - \frac{2}{41} + \frac{23}{41} i

(37) (43)

(x + 3 y + 5 z)^{2}

(2 + 2 i)^{8}

- \frac{7}{3}

- \frac{7}{4}