What is (5-12i)/(2i-3) ?

The solution to (5-12i)/(2i-3) is -3+2i

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simplify (5-12i)/(2i-3)

simplify

\frac{5 - 12 i}{2 i - 3}

- 3 + 2 i

Solution steps

\frac{5 - 12 i}{2 i - 3}

Rewrite

2 i - 3

in standard complex form:

- 3 + 2 i

= \frac{5 - 12 i}{- 3 + 2 i}

Multiply by the conjugate

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

= \frac{( 5 - 12 i ) ( - 3 - 2 i )}{( - 3 + 2 i ) ( - 3 - 2 i )}

Simplify

\frac{( 5 - 12 i ) ( - 3 - 2 i )}{( - 3 + 2 i ) ( - 3 - 2 i )} : \frac{- 39 + 26 i}{13}

= \frac{- 39 + 26 i}{13}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{- 39}{13} + \frac{26}{13} i

Simplify

\frac{- 39}{13} + \frac{26}{13} i : - 3 + 2 i

= - 3 + 2 i

\frac{b ^{4} - 1}{b ^{2} - 1}

\frac{x - 3}{x + 1} > 0

x^{2} - 4 x - 21

x^{5} - 5 x^{3} + 4 x

(1 - i)^{3}