Write in Standard Form (9-17i)/(1-3i)

$\frac{9 - 17 i}{1 - 3 i}$

Step 1

Multiply the numerator and denominator of $\frac{9 - 17 i}{1 - 3 i}$ by the conjugate of $1 - 3 i$ to make the denominator real.

$\frac{9 - 17 i}{1 - 3 i} \cdot \frac{1 + 3 i}{1 + 3 i}$

Step 2

Multiply.

Combine.

$\frac{(9 - 17 i) (1 + 3 i)}{(1 - 3 i) (1 + 3 i)}$

Simplify the numerator.

Expand $(9 - 17 i) (1 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{9 (1 + 3 i) - 17 i (1 + 3 i)}{(1 - 3 i) (1 + 3 i)}$

Apply the distributive property.

$\frac{9 \cdot 1 + 9 (3 i) - 17 i (1 + 3 i)}{(1 - 3 i) (1 + 3 i)}$

Apply the distributive property.

$\frac{9 \cdot 1 + 9 (3 i) - 17 i \cdot 1 - 17 i (3 i)}{(1 - 3 i) (1 + 3 i)}$

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $1$ .

$\frac{9 + 9 (3 i) - 17 i \cdot 1 - 17 i (3 i)}{(1 - 3 i) (1 + 3 i)}$

Multiply $3$ by $9$ .

$\frac{9 + 27 i - 17 i \cdot 1 - 17 i (3 i)}{(1 - 3 i) (1 + 3 i)}$

Multiply $- 17$ by $1$ .

$\frac{9 + 27 i - 17 i - 17 i (3 i)}{(1 - 3 i) (1 + 3 i)}$

Multiply $- 17 i (3 i)$ .

Multiply $3$ by $- 17$ .

$\frac{9 + 27 i - 17 i - 51 i i}{(1 - 3 i) (1 + 3 i)}$

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

$\frac{9 + 27 i - 17 i - 51 (i^{1} i)}{(1 - 3 i) (1 + 3 i)}$

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

$\frac{9 + 27 i - 17 i - 51 (i^{1} i^{1})}{(1 - 3 i) (1 + 3 i)}$

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

$\frac{9 + 27 i - 17 i - 51 i^{1 + 1}}{(1 - 3 i) (1 + 3 i)}$

Add $1$ and $1$ .

$\frac{9 + 27 i - 17 i - 51 i^{2}}{(1 - 3 i) (1 + 3 i)}$

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

$\frac{9 + 27 i - 17 i - 51 \cdot - 1}{(1 - 3 i) (1 + 3 i)}$

Multiply $- 51$ by $- 1$ .

$\frac{9 + 27 i - 17 i + 51}{(1 - 3 i) (1 + 3 i)}$

Add $9$ and $51$ .

$\frac{60 + 27 i - 17 i}{(1 - 3 i) (1 + 3 i)}$

Subtract $17 i$ from $27 i$ .

$\frac{60 + 10 i}{(1 - 3 i) (1 + 3 i)}$

Simplify the denominator.

Expand $(1 - 3 i) (1 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{60 + 10 i}{1 (1 + 3 i) - 3 i (1 + 3 i)}$

Apply the distributive property.

$\frac{60 + 10 i}{1 \cdot 1 + 1 (3 i) - 3 i (1 + 3 i)}$

Apply the distributive property.

$\frac{60 + 10 i}{1 \cdot 1 + 1 (3 i) - 3 i \cdot 1 - 3 i (3 i)}$

Simplify.

Multiply $1$ by $1$ .

$\frac{60 + 10 i}{1 + 1 (3 i) - 3 i \cdot 1 - 3 i (3 i)}$

Multiply $3$ by $1$ .

$\frac{60 + 10 i}{1 + 3 i - 3 i \cdot 1 - 3 i (3 i)}$

Multiply $- 3$ by $1$ .

$\frac{60 + 10 i}{1 + 3 i - 3 i - 3 i (3 i)}$

Multiply $3$ by $- 3$ .

$\frac{60 + 10 i}{1 + 3 i - 3 i - 9 i i}$

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

$\frac{60 + 10 i}{1 + 3 i - 3 i - 9 (i^{1} i)}$

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

$\frac{60 + 10 i}{1 + 3 i - 3 i - 9 (i^{1} i^{1})}$

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

$\frac{60 + 10 i}{1 + 3 i - 3 i - 9 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{60 + 10 i}{1 + 3 i - 3 i - 9 i^{2}}$

Subtract $3 i$ from $3 i$ .

$\frac{60 + 10 i}{1 + 0 - 9 i^{2}}$

Add $1$ and $0$ .

$\frac{60 + 10 i}{1 - 9 i^{2}}$

Simplify each term.

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

$\frac{60 + 10 i}{1 - 9 \cdot - 1}$

Multiply $- 9$ by $- 1$ .

$\frac{60 + 10 i}{1 + 9}$

Add $1$ and $9$ .

$\frac{60 + 10 i}{10}$

Step 3

Cancel the common factor of $60 + 10 i$ and $10$ .

Factor $10$ out of $60$ .

$\frac{10 \cdot 6 + 10 i}{10}$

Factor $10$ out of $10 i$ .

$\frac{10 \cdot 6 + 10 (i)}{10}$

Factor $10$ out of $10 (6) + 10 (i)$ .

$\frac{10 (6 + i)}{10}$

Cancel the common factors.

Factor $10$ out of $10$ .

$\frac{10 (6 + i)}{10 (1)}$

Cancel the common factor.

$\frac{10 (6 + i)}{10 \cdot 1}$

Rewrite the expression.

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

Divide $6 + i$ by $1$ .

$6 + i$

Write in Standard Form (9-17i)/(1-3i)

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