Write in Standard Form 2/(7-8i)

$\frac{2}{7 - 8 i}$

Step 1

Multiply the numerator and denominator of $\frac{2}{7 - 8 i}$ by the conjugate of $7 - 8 i$ to make the denominator real.

$\frac{2}{7 - 8 i} \cdot \frac{7 + 8 i}{7 + 8 i}$

Step 2

Multiply.

Combine.

$\frac{2 (7 + 8 i)}{(7 - 8 i) (7 + 8 i)}$

Simplify the numerator.

Apply the distributive property.

$\frac{2 \cdot 7 + 2 (8 i)}{(7 - 8 i) (7 + 8 i)}$

Multiply $2$ by $7$ .

$\frac{14 + 2 (8 i)}{(7 - 8 i) (7 + 8 i)}$

Multiply $8$ by $2$ .

$\frac{14 + 16 i}{(7 - 8 i) (7 + 8 i)}$

Simplify the denominator.

Expand $(7 - 8 i) (7 + 8 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{14 + 16 i}{7 (7 + 8 i) - 8 i (7 + 8 i)}$

Apply the distributive property.

$\frac{14 + 16 i}{7 \cdot 7 + 7 (8 i) - 8 i (7 + 8 i)}$

Apply the distributive property.

$\frac{14 + 16 i}{7 \cdot 7 + 7 (8 i) - 8 i \cdot 7 - 8 i (8 i)}$

Simplify.

Multiply $7$ by $7$ .

$\frac{14 + 16 i}{49 + 7 (8 i) - 8 i \cdot 7 - 8 i (8 i)}$

Multiply $8$ by $7$ .

$\frac{14 + 16 i}{49 + 56 i - 8 i \cdot 7 - 8 i (8 i)}$

Multiply $7$ by $- 8$ .

$\frac{14 + 16 i}{49 + 56 i - 56 i - 8 i (8 i)}$

Multiply $8$ by $- 8$ .

$\frac{14 + 16 i}{49 + 56 i - 56 i - 64 i i}$

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

$\frac{14 + 16 i}{49 + 56 i - 56 i - 64 (i^{1} i)}$

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

$\frac{14 + 16 i}{49 + 56 i - 56 i - 64 (i^{1} i^{1})}$

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

$\frac{14 + 16 i}{49 + 56 i - 56 i - 64 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{14 + 16 i}{49 + 56 i - 56 i - 64 i^{2}}$

Subtract $56 i$ from $56 i$ .

$\frac{14 + 16 i}{49 + 0 - 64 i^{2}}$

Add $49$ and $0$ .

$\frac{14 + 16 i}{49 - 64 i^{2}}$

Simplify each term.

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

$\frac{14 + 16 i}{49 - 64 \cdot - 1}$

Multiply $- 64$ by $- 1$ .

$\frac{14 + 16 i}{49 + 64}$

Add $49$ and $64$ .

$\frac{14 + 16 i}{113}$

Step 3

Split the fraction $\frac{14 + 16 i}{113}$ into two fractions.

$\frac{14}{113} + \frac{16 i}{113}$

Write in Standard Form 2/(7-8i)

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