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

The solution to (4+5i)/(2-3i) is -7/13+22/13 i

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

simplify

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

- \frac{7}{13} + \frac{22}{13} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{( 4 + 5 i ) ( 2 + 3 i )}{( 2 - 3 i ) ( 2 + 3 i )} : \frac{- 7 + 22 i}{13}

= \frac{- 7 + 22 i}{13}

Rewrite in standard complex form:

- \frac{7}{13} + \frac{22}{13} i

= - \frac{7}{13} + \frac{22}{13} i

- 16 \cdot 2

- 7 + (1)

(2 - 3 i) (4 + 2 i)

\frac{x ^{2} - 2 x}{x ^{2} - 4}

37 \cdot 3