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

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

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

simplify

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

- \frac{1}{5} - \frac{7}{5} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

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

= \frac{- 1 - 7 i}{5}

Apply the fraction rule:

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

= \frac{- 1}{5} + \frac{- 7}{5} i

Simplify

\frac{- 1}{5} + \frac{- 7}{5} i : - \frac{1}{5} - \frac{7}{5} i

= - \frac{1}{5} - \frac{7}{5} i

\frac{41 \cdot 1 0 ^{- 9}}{2.7 \cdot 1 0 ^{- 12}}

- 3 x \geq - 18

X^{2} + 2 X - 5 = 0

- x^{2} - 5 x - 6

lo g_{3} (48) - 2 lo g_{3} (4)