Basic Math Examples

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

Step 1

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

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Step 1.1

Factor $3$ out of $- 3$ .

$\frac{3 (- 1) - 12 i}{6 i}$

Step 1.2

Factor $3$ out of $- 12 i$ .

$\frac{3 (- 1) + 3 (- 4 i)}{6 i}$

Step 1.3

Factor $3$ out of $3 (- 1) + 3 (- 4 i)$ .

$\frac{3 (- 1 - 4 i)}{6 i}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $3$ out of $6 i$ .

$\frac{3 (- 1 - 4 i)}{3 (2 i)}$

Step 1.4.2

Cancel the common factor.

$\frac{3 (- 1 - 4 i)}{3 (2 i)}$

Step 1.4.3

Rewrite the expression.

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

Step 2

Multiply the numerator and denominator of $\frac{- 1 - 4 i}{2 i}$ by the conjugate of $2 i$ to make the denominator real.

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

Step 3

Multiply.

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Step 3.1

Combine.

$\frac{(- 1 - 4 i) i}{2 i i}$

Step 3.2

Simplify the numerator.

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Step 3.2.1

Apply the distributive property.

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

Step 3.2.2

Rewrite $- 1 i$ as $- i$ .

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

Step 3.2.3

Multiply $- 4 i i$ .

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Step 3.2.3.1

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

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

Step 3.2.3.2

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

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

Step 3.2.3.3

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

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

Step 3.2.3.4

Add $1$ and $1$ .

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

Step 3.2.4

Simplify each term.

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Step 3.2.4.1

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

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

Step 3.2.4.2

Multiply $- 4$ by $- 1$ .

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

Step 3.2.5

Reorder $- i$ and $4$ .

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

Step 3.3

Simplify the denominator.

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Step 3.3.1

Add parentheses.

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

Step 3.3.2

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

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

Step 3.3.3

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

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

Step 3.3.4

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

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

Step 3.3.5

Add $1$ and $1$ .

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

Step 3.3.6

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

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

Step 4

Multiply $2$ by $- 1$ .

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

Step 5

Split the fraction $\frac{4 - i}{- 2}$ into two fractions.

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

Step 6

Simplify each term.

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Step 6.1

Divide $4$ by $- 2$ .

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

Step 6.2

Dividing two negative values results in a positive value.

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