What is (2-3i)/(1+2i) ?

The solution to (2-3i)/(1+2i) is -4/5-7/5 i

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simplify (2-3i)/(1+2i)

simplify

\frac{2 - 3 i}{1 + 2 i}

- \frac{4}{5} - \frac{7}{5} i

Solution steps

\frac{2 - 3 i}{1 + 2 i}

Multiply by the conjugate

\frac{1 - 2 i}{1 - 2 i}

= \frac{( 2 - 3 i ) ( 1 - 2 i )}{( 1 + 2 i ) ( 1 - 2 i )}

Simplify

\frac{( 2 - 3 i ) ( 1 - 2 i )}{( 1 + 2 i ) ( 1 - 2 i )} : \frac{- 4 - 7 i}{5}

= \frac{- 4 - 7 i}{5}

Apply the fraction rule:

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

= \frac{- 4}{5} + \frac{- 7}{5} i

Simplify

\frac{- 4}{5} + \frac{- 7}{5} i : - \frac{4}{5} - \frac{7}{5} i

= - \frac{4}{5} - \frac{7}{5} i

12 x - (- 4 x - 6) = 3 x - (9 x - 27)

3 x^{2} + 16 x - 35 = 0

x^{2} = 31

- 3 - \frac{1}{2}

\frac{[ ( \frac{6 - 11 x}{2} ) ]}{( x - 3 )} > \frac{- 1}{2 ( x + 12 )}