Write in Standard Form 2/(6-i)

$\frac{2}{6 - i}$

Step 1

Multiply the numerator and denominator of $\frac{2}{6 - i}$ by the conjugate of $6 - i$ to make the denominator real.

$\frac{2}{6 - i} \cdot \frac{6 + i}{6 + i}$

Step 2

Multiply.

Combine.

$\frac{2 (6 + i)}{(6 - i) (6 + i)}$

Simplify the numerator.

Apply the distributive property.

$\frac{2 \cdot 6 + 2 i}{(6 - i) (6 + i)}$

Multiply $2$ by $6$ .

$\frac{12 + 2 i}{(6 - i) (6 + i)}$

Simplify the denominator.

Expand $(6 - i) (6 + i)$ using the FOIL Method.

Apply the distributive property.

$\frac{12 + 2 i}{6 (6 + i) - i (6 + i)}$

Apply the distributive property.

$\frac{12 + 2 i}{6 \cdot 6 + 6 i - i (6 + i)}$

Apply the distributive property.

$\frac{12 + 2 i}{6 \cdot 6 + 6 i - i \cdot 6 - i i}$

Simplify.

Multiply $6$ by $6$ .

$\frac{12 + 2 i}{36 + 6 i - i \cdot 6 - i i}$

Multiply $6$ by $- 1$ .

$\frac{12 + 2 i}{36 + 6 i - 6 i - i i}$

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

$\frac{12 + 2 i}{36 + 6 i - 6 i - (i^{1} i)}$

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

$\frac{12 + 2 i}{36 + 6 i - 6 i - (i^{1} i^{1})}$

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

$\frac{12 + 2 i}{36 + 6 i - 6 i - i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{12 + 2 i}{36 + 6 i - 6 i - i^{2}}$

Subtract $6 i$ from $6 i$ .

$\frac{12 + 2 i}{36 + 0 - i^{2}}$

Add $36$ and $0$ .

$\frac{12 + 2 i}{36 - i^{2}}$

Simplify each term.

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

$\frac{12 + 2 i}{36 - - 1}$

Multiply $- 1$ by $- 1$ .

$\frac{12 + 2 i}{36 + 1}$

Add $36$ and $1$ .

$\frac{12 + 2 i}{37}$

Step 3

Split the fraction $\frac{12 + 2 i}{37}$ into two fractions.

$\frac{12}{37} + \frac{2 i}{37}$

Write in Standard Form 2/(6-i)

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