Simplify (8+4i)/(2i)

$\frac{8 + 4 i}{2 i}$

Cancel the common factor of $8 + 4 i$ and $2$ .

Factor $2$ out of $8$ .

$\frac{2 \cdot 4 + 4 i}{2 i}$

Factor $2$ out of $4 i$ .

$\frac{2 \cdot 4 + 2 (2 i)}{2 i}$

Factor $2$ out of $2 (4) + 2 (2 i)$ .

$\frac{2 (4 + 2 i)}{2 i}$

Cancel the common factors.

Factor $2$ out of $2 i$ .

$\frac{2 (4 + 2 i)}{2 (i)}$

Cancel the common factor.

$\frac{2 (4 + 2 i)}{2 i}$

Rewrite the expression.

$\frac{4 + 2 i}{i}$

Multiply the numerator and denominator of $\frac{4 + 2 i}{i}$ by the conjugate of $i$ to make the denominator real.

$\frac{4 + 2 i}{i} \cdot \frac{i}{i}$

Multiply.

Combine.

$\frac{(4 + 2 i) i}{i i}$

Simplify the numerator.

Apply the distributive property.

$\frac{4 i + 2 i i}{i i}$

Multiply $2 i i$ .

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

$\frac{4 i + 2 (i^{1} i)}{i i}$

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

$\frac{4 i + 2 (i^{1} i^{1})}{i i}$

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

$\frac{4 i + 2 i^{1 + 1}}{i i}$

Add $1$ and $1$ .

$\frac{4 i + 2 i^{2}}{i i}$

Simplify each term.

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

$\frac{4 i + 2 \cdot - 1}{i i}$

Multiply $2$ by $- 1$ .

$\frac{4 i - 2}{i i}$

Reorder $4 i$ and $- 2$ .

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

Simplify the denominator.

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

$\frac{- 2 + 4 i}{i^{1} i}$

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

$\frac{- 2 + 4 i}{i^{1} i^{1}}$

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

$\frac{- 2 + 4 i}{i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 2 + 4 i}{i^{2}}$

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

$\frac{- 2 + 4 i}{- 1}$

Simplify the expression.

Move the negative one from the denominator of $\frac{- 2 + 4 i}{- 1}$ .

$- 1 \cdot (- 2 + 4 i)$

Rewrite $- 1 \cdot (- 2 + 4 i)$ as $- (- 2 + 4 i)$ .

$- (- 2 + 4 i)$

Apply the distributive property.

$- - 2 - (4 i)$

Multiply.

Multiply $- 1$ by $- 2$ .

$2 - (4 i)$

Multiply $4$ by $- 1$ .

$2 - 4 i$

Simplify (8+4i)/(2i)

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