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

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

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

simplify

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

\frac{1}{5} + \frac{2}{5} i

Solution steps

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

Multiply by the conjugate

\frac{4 + 3 i}{4 + 3 i}

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

Simplify

\frac{( 2 + i ) ( 4 + 3 i )}{( 4 - 3 i ) ( 4 + 3 i )} : \frac{5 + 10 i}{25}

= \frac{5 + 10 i}{25}

Apply the fraction rule:

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

= \frac{5}{25} + \frac{10}{25} i

Simplify

\frac{5}{25} + \frac{10}{25} i : \frac{1}{5} + \frac{2}{5} i

= \frac{1}{5} + \frac{2}{5} i

5 t^{2} - 24 t - 5

- 8 \leq 5 x - 9 \leq 5

5 x^{2} y^{- 3}

\frac{1}{4} (8 - 4 p) + 2 p = 12

(t - 1)^{2} (t + 4) (11 - t) > 0