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Popular >

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

Solution

simplify

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

Solution

1 - 2 i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

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

= \frac{5 - 10 i}{5}

Apply the fraction rule:

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

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

Simplify

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

= 1 - 2 i

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Frequently Asked Questions (FAQ)

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