Simplify (2+i)/i

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

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

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

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Reorder $2 i$ and $- 1$ .

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

Simplify the denominator.

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Simplify the expression.

Move the negative one from the denominator of $\frac{- 1 + 2 i}{- 1}$ .

$- 1 \cdot (- 1 + 2 i)$

Rewrite $- 1 \cdot (- 1 + 2 i)$ as $- (- 1 + 2 i)$ .

$- (- 1 + 2 i)$

Apply the distributive property.

$- - 1 - (2 i)$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 - (2 i)$

Multiply $2$ by $- 1$ .

$1 - 2 i$