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

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

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

simplify

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

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

Solution steps

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

Rewrite

i + 2

in standard complex form:

2 + i

Rewrite

i - 1

in standard complex form:

- 1 + i

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

Multiply by the conjugate

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

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

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

\frac{4}{7 - 5}

- 5 0^{2}

58 \times 34

\frac{5}{8} \times \frac{1}{2}

lo g_{16} (\frac{1}{32})