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

The solution to (2+3i)/(4-5i) is -7/41+22/41 i

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

simplify

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

- \frac{7}{41} + \frac{22}{41} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{( 2 + 3 i ) ( 4 + 5 i )}{( 4 - 5 i ) ( 4 + 5 i )} : \frac{- 7 + 22 i}{41}

= \frac{- 7 + 22 i}{41}

Rewrite in standard complex form:

- \frac{7}{41} + \frac{22}{41} i

= - \frac{7}{41} + \frac{22}{41} i

- 24 a^{x + 2} - 15 a^{x + 2} + 39 a^{x + 2}

27 m^{3} + 125 n^{3}

1 + \frac{4}{9}

(8 x^{2} - 1)^{2}

(1 + x - 4 x^{2}) (1 + 2 x + 3 x^{2}) (1 - 2 x + 4 x^{2})