Simplify (-5+i)/(2i)

$\frac{- 5 + i}{2 i}$

Multiply the numerator and denominator of $\frac{- 5 + i}{2 i}$ by the conjugate of $2 i$ to make the denominator real.

$\frac{- 5 + i}{2 i} \cdot \frac{i}{i}$

Multiply.

Combine.

$\frac{(- 5 + i) i}{2 i i}$

Simplify the numerator.

Apply the distributive property.

$\frac{- 5 i + i i}{2 i i}$

Multiply $i i$ .

Raise $i$ to the power of $1$ .

$\frac{- 5 i + i^{1} i}{2 i i}$

Raise $i$ to the power of $1$ .

$\frac{- 5 i + i^{1} i^{1}}{2 i i}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 5 i + i^{1 + 1}}{2 i i}$

Add $1$ and $1$ .

$\frac{- 5 i + i^{2}}{2 i i}$

Rewrite $i^{2}$ as $- 1$ .

$\frac{- 5 i - 1}{2 i i}$

Reorder $- 5 i$ and $- 1$ .

$\frac{- 1 - 5 i}{2 i i}$

Simplify the denominator.

Add parentheses.

$\frac{- 1 - 5 i}{2 (i i)}$

Raise $i$ to the power of $1$ .

$\frac{- 1 - 5 i}{2 (i^{1} i)}$

Raise $i$ to the power of $1$ .

$\frac{- 1 - 5 i}{2 (i^{1} i^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 1 - 5 i}{2 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 1 - 5 i}{2 i^{2}}$

Rewrite $i^{2}$ as $- 1$ .

$\frac{- 1 - 5 i}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$\frac{- 1 - 5 i}{- 2}$

Split the fraction $\frac{- 1 - 5 i}{- 2}$ into two fractions.

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

Simplify each term.

Dividing two negative values results in a positive value.

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

Dividing two negative values results in a positive value.

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