Divide (4+i)/(8i)

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

Step 1

Multiply the numerator and denominator of $\frac{4 + i}{8 i}$ by the conjugate of $8 i$ to make the denominator real.

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

Step 2

Multiply.

Combine.

$\frac{(4 + i) i}{8 i i}$

Simplify the numerator.

Apply the distributive property.

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

Multiply $i i$ .

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

$\frac{4 i + i^{1} i}{8 i i}$

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

$\frac{4 i + i^{1} i^{1}}{8 i i}$

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

$\frac{4 i + i^{1 + 1}}{8 i i}$

Add $1$ and $1$ .

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

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

$\frac{4 i - 1}{8 i i}$

Reorder $4 i$ and $- 1$ .

$\frac{- 1 + 4 i}{8 i i}$

Simplify the denominator.

Add parentheses.

$\frac{- 1 + 4 i}{8 (i i)}$

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

$\frac{- 1 + 4 i}{8 (i^{1} i)}$

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

$\frac{- 1 + 4 i}{8 (i^{1} i^{1})}$

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

$\frac{- 1 + 4 i}{8 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 1 + 4 i}{8 i^{2}}$

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

$\frac{- 1 + 4 i}{8 \cdot - 1}$

Step 3

Multiply $8$ by $- 1$ .

$\frac{- 1 + 4 i}{- 8}$

Step 4

Split the fraction $\frac{- 1 + 4 i}{- 8}$ into two fractions.

$\frac{- 1}{- 8} + \frac{4 i}{- 8}$

Step 5

Simplify each term.

Dividing two negative values results in a positive value.

$\frac{1}{8} + \frac{4 i}{- 8}$

Cancel the common factor of $4$ and $- 8$ .

Factor $4$ out of $4 i$ .

$\frac{1}{8} + \frac{4 (i)}{- 8}$

Cancel the common factors.

Factor $4$ out of $- 8$ .

$\frac{1}{8} + \frac{4 i}{4 \cdot - 2}$

Cancel the common factor.

$\frac{1}{8} + \frac{4 i}{4 \cdot - 2}$

Rewrite the expression.

$\frac{1}{8} + \frac{i}{- 2}$

Move the negative in front of the fraction.

$\frac{1}{8} - \frac{i}{2}$

Divide (4+i)/(8i)

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