Finite Math Examples

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

Step 1

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

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

Step 2

Multiply.

Tap for more steps...

Step 2.1

Combine.

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

Step 2.2

Simplify the numerator.

Tap for more steps...

Step 2.2.1

Apply the distributive property.

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

Step 2.2.2

Multiply $4$ by $8$ .

$\frac{32 + 4 i}{(8 - i) (8 + i)}$

Step 2.3

Simplify the denominator.

Tap for more steps...

Step 2.3.1

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

Tap for more steps...

Step 2.3.1.1

Apply the distributive property.

$\frac{32 + 4 i}{8 (8 + i) - i (8 + i)}$

Step 2.3.1.2

Apply the distributive property.

$\frac{32 + 4 i}{8 \cdot 8 + 8 i - i (8 + i)}$

Step 2.3.1.3

Apply the distributive property.

$\frac{32 + 4 i}{8 \cdot 8 + 8 i - i \cdot 8 - i i}$

Step 2.3.2

Simplify.

Tap for more steps...

Step 2.3.2.1

Multiply $8$ by $8$ .

$\frac{32 + 4 i}{64 + 8 i - i \cdot 8 - i i}$

Step 2.3.2.2

Multiply $8$ by $- 1$ .

$\frac{32 + 4 i}{64 + 8 i - 8 i - i i}$

Step 2.3.2.3

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

$\frac{32 + 4 i}{64 + 8 i - 8 i - (i^{1} i)}$

Step 2.3.2.4

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

$\frac{32 + 4 i}{64 + 8 i - 8 i - (i^{1} i^{1})}$

Step 2.3.2.5

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

$\frac{32 + 4 i}{64 + 8 i - 8 i - i^{1 + 1}}$

Step 2.3.2.6

Add $1$ and $1$ .

$\frac{32 + 4 i}{64 + 8 i - 8 i - i^{2}}$

Step 2.3.2.7

Subtract $8 i$ from $8 i$ .

$\frac{32 + 4 i}{64 + 0 - i^{2}}$

Step 2.3.2.8

Add $64$ and $0$ .

$\frac{32 + 4 i}{64 - i^{2}}$

Step 2.3.3

Simplify each term.

Tap for more steps...

Step 2.3.3.1

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

$\frac{32 + 4 i}{64 - - 1}$

Step 2.3.3.2

Multiply $- 1$ by $- 1$ .

$\frac{32 + 4 i}{64 + 1}$

Step 2.3.4

Add $64$ and $1$ .

$\frac{32 + 4 i}{65}$

Step 3

Split the fraction $\frac{32 + 4 i}{65}$ into two fractions.

$\frac{32}{65} + \frac{4 i}{65}$