Simplify (6+12i)/(3i)

$\frac{6 + 12 i}{3 i}$

Step 1

Cancel the common factor of $6 + 12 i$ and $3$ .

Factor $3$ out of $6$ .

$\frac{3 \cdot 2 + 12 i}{3 i}$

Factor $3$ out of $12 i$ .

$\frac{3 \cdot 2 + 3 (4 i)}{3 i}$

Factor $3$ out of $3 (2) + 3 (4 i)$ .

$\frac{3 (2 + 4 i)}{3 i}$

Cancel the common factors.

Factor $3$ out of $3 i$ .

$\frac{3 (2 + 4 i)}{3 (i)}$

Cancel the common factor.

$\frac{3 (2 + 4 i)}{3 i}$

Rewrite the expression.

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

Step 2

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

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

Step 3

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $4 i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

Simplify each term.

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

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

Multiply $4$ by $- 1$ .

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

Reorder $2 i$ and $- 4$ .

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

Simplify the denominator.

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Step 4

Simplify the expression.

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

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

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

$- (- 4 + 2 i)$

Step 5

Apply the distributive property.

$- - 4 - (2 i)$

Step 6

Multiply.

Multiply $- 1$ by $- 4$ .

$4 - (2 i)$

Multiply $2$ by $- 1$ .

$4 - 2 i$

Simplify (6+12i)/(3i)

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