Basic Math Examples

$\frac{16 + 4 i}{- 16 i}$

Step 1

Cancel the common factor of $16 + 4 i$ and $- 16$ .

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Step 1.1

Factor $4$ out of $16$ .

$\frac{4 \cdot 4 + 4 i}{- 16 i}$

Step 1.2

Factor $4$ out of $4 i$ .

$\frac{4 \cdot 4 + 4 (i)}{- 16 i}$

Step 1.3

Factor $4$ out of $4 \cdot 4 + 4 (i)$ .

$\frac{4 \cdot (4 + i)}{- 16 i}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $4$ out of $- 16 i$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 2

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

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

Step 3

Multiply.

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Step 3.1

Combine.

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

Step 3.2

Simplify the numerator.

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Step 3.2.1

Apply the distributive property.

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

Step 3.2.2

Multiply $i i$ .

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Step 3.2.2.1

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

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

Step 3.2.2.2

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

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

Step 3.2.2.3

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

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

Step 3.2.2.4

Add $1$ and $1$ .

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

Step 3.2.3

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

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

Step 3.2.4

Reorder $4 i$ and $- 1$ .

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

Step 3.3

Simplify the denominator.

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Step 3.3.1

Add parentheses.

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

Step 3.3.2

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

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

Step 3.3.3

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

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

Step 3.3.4

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

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

Step 3.3.5

Add $1$ and $1$ .

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

Step 3.3.6

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

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

Step 4

Multiply $- 4$ by $- 1$ .

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

Step 5

Split the fraction $\frac{- 1 + 4 i}{4}$ into two fractions.

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

Step 6

Simplify each term.

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Step 6.1

Move the negative in front of the fraction.

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

Step 6.2

Cancel the common factor of $4$ .

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Step 6.2.1

Cancel the common factor.

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

Step 6.2.2

Divide $i$ by $1$ .

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