Write in Standard Form 6/(1-i)

$\frac{6}{1 - i}$

Step 1

Multiply the numerator and denominator of $\frac{6}{1 - i}$ by the conjugate of $1 - i$ to make the denominator real.

$\frac{6}{1 - i} \cdot \frac{1 + i}{1 + i}$

Step 2

Multiply.

Combine.

$\frac{6 (1 + i)}{(1 - i) (1 + i)}$

Simplify the numerator.

Apply the distributive property.

$\frac{6 \cdot 1 + 6 i}{(1 - i) (1 + i)}$

Multiply $6$ by $1$ .

$\frac{6 + 6 i}{(1 - i) (1 + i)}$

Simplify the denominator.

Expand $(1 - i) (1 + i)$ using the FOIL Method.

Apply the distributive property.

$\frac{6 + 6 i}{1 (1 + i) - i (1 + i)}$

Apply the distributive property.

$\frac{6 + 6 i}{1 \cdot 1 + 1 i - i (1 + i)}$

Apply the distributive property.

$\frac{6 + 6 i}{1 \cdot 1 + 1 i - i \cdot 1 - i i}$

Simplify.

Multiply $1$ by $1$ .

$\frac{6 + 6 i}{1 + 1 i - i \cdot 1 - i i}$

Multiply $- 1$ by $1$ .

$\frac{6 + 6 i}{1 + 1 i - i - i i}$

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

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

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

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

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

$\frac{6 + 6 i}{1 + 1 i - i - i^{1 + 1}}$

Add $1$ and $1$ .

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

Subtract $i$ from $1 i$ .

$\frac{6 + 6 i}{1 + 0 - i^{2}}$

Add $1$ and $0$ .

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

Simplify each term.

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

$\frac{6 + 6 i}{1 - - 1}$

Multiply $- 1$ by $- 1$ .

$\frac{6 + 6 i}{1 + 1}$

Add $1$ and $1$ .

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

Step 3

Cancel the common factor of $6 + 6 i$ and $2$ .

Factor $2$ out of $6$ .

$\frac{2 \cdot 3 + 6 i}{2}$

Factor $2$ out of $6 i$ .

$\frac{2 \cdot 3 + 2 (3 i)}{2}$

Factor $2$ out of $2 (3) + 2 (3 i)$ .

$\frac{2 (3 + 3 i)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (3 + 3 i)}{2 (1)}$

Cancel the common factor.

$\frac{2 (3 + 3 i)}{2 \cdot 1}$

Rewrite the expression.

$\frac{3 + 3 i}{1}$

Divide $3 + 3 i$ by $1$ .

$3 + 3 i$

Write in Standard Form 6/(1-i)

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