Write in Standard Form 9/(8-i)

$\frac{9}{8 - i}$

Step 1

Multiply the numerator and denominator of $\frac{9}{8 - i}$ by the conjugate of $8 - i$ to make the denominator real.

$\frac{9}{8 - i} \cdot \frac{8 + i}{8 + i}$

Step 2

Multiply.

Combine.

$\frac{9 (8 + i)}{(8 - i) (8 + i)}$

Simplify the numerator.

Apply the distributive property.

$\frac{9 \cdot 8 + 9 i}{(8 - i) (8 + i)}$

Multiply $9$ by $8$ .

$\frac{72 + 9 i}{(8 - i) (8 + i)}$

Simplify the denominator.

Expand $(8 - i) (8 + i)$ using the FOIL Method.

Apply the distributive property.

$\frac{72 + 9 i}{8 (8 + i) - i (8 + i)}$

Apply the distributive property.

$\frac{72 + 9 i}{8 \cdot 8 + 8 i - i (8 + i)}$

Apply the distributive property.

$\frac{72 + 9 i}{8 \cdot 8 + 8 i - i \cdot 8 - i i}$

Simplify.

Multiply $8$ by $8$ .

$\frac{72 + 9 i}{64 + 8 i - i \cdot 8 - i i}$

Multiply $8$ by $- 1$ .

$\frac{72 + 9 i}{64 + 8 i - 8 i - i i}$

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

$\frac{72 + 9 i}{64 + 8 i - 8 i - (i^{1} i)}$

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

$\frac{72 + 9 i}{64 + 8 i - 8 i - (i^{1} i^{1})}$

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

$\frac{72 + 9 i}{64 + 8 i - 8 i - i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{72 + 9 i}{64 + 8 i - 8 i - i^{2}}$

Subtract $8 i$ from $8 i$ .

$\frac{72 + 9 i}{64 + 0 - i^{2}}$

Add $64$ and $0$ .

$\frac{72 + 9 i}{64 - i^{2}}$

Simplify each term.

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

$\frac{72 + 9 i}{64 - - 1}$

Multiply $- 1$ by $- 1$ .

$\frac{72 + 9 i}{64 + 1}$

Add $64$ and $1$ .

$\frac{72 + 9 i}{65}$

Step 3

Split the fraction $\frac{72 + 9 i}{65}$ into two fractions.

$\frac{72}{65} + \frac{9 i}{65}$

Write in Standard Form 9/(8-i)

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