Write in Standard Form (66+3i)/(3-6i)

$\frac{66 + 3 i}{3 - 6 i}$

Step 1

Cancel the common factor of $66 + 3 i$ and $3 - 6 i$ .

Factor $3$ out of $66$ .

$\frac{3 \cdot 22 + 3 i}{3 - 6 i}$

Factor $3$ out of $3 i$ .

$\frac{3 \cdot 22 + 3 (i)}{3 - 6 i}$

Factor $3$ out of $3 (22) + 3 (i)$ .

$\frac{3 (22 + i)}{3 - 6 i}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (22 + i)}{3 (1) - 6 i}$

Factor $3$ out of $- 6 i$ .

$\frac{3 (22 + i)}{3 (1) + 3 (- 2 i)}$

Factor $3$ out of $3 (1) + 3 (- 2 i)$ .

$\frac{3 (22 + i)}{3 (1 - 2 i)}$

Cancel the common factor.

$\frac{3 (22 + i)}{3 (1 - 2 i)}$

Rewrite the expression.

$\frac{22 + i}{1 - 2 i}$

Step 2

Multiply the numerator and denominator of $\frac{22 + i}{1 - 2 i}$ by the conjugate of $1 - 2 i$ to make the denominator real.

$\frac{22 + i}{1 - 2 i} \cdot \frac{1 + 2 i}{1 + 2 i}$

Step 3

Multiply.

Combine.

$\frac{(22 + i) (1 + 2 i)}{(1 - 2 i) (1 + 2 i)}$

Simplify the numerator.

Expand $(22 + i) (1 + 2 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{22 (1 + 2 i) + i (1 + 2 i)}{(1 - 2 i) (1 + 2 i)}$

Apply the distributive property.

$\frac{22 \cdot 1 + 22 (2 i) + i (1 + 2 i)}{(1 - 2 i) (1 + 2 i)}$

Apply the distributive property.

$\frac{22 \cdot 1 + 22 (2 i) + i \cdot 1 + i (2 i)}{(1 - 2 i) (1 + 2 i)}$

Simplify and combine like terms.

Simplify each term.

Multiply $22$ by $1$ .

$\frac{22 + 22 (2 i) + i \cdot 1 + i (2 i)}{(1 - 2 i) (1 + 2 i)}$

Multiply $2$ by $22$ .

$\frac{22 + 44 i + i \cdot 1 + i (2 i)}{(1 - 2 i) (1 + 2 i)}$

Multiply $i$ by $1$ .

$\frac{22 + 44 i + i + i (2 i)}{(1 - 2 i) (1 + 2 i)}$

Multiply $i (2 i)$ .

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

$\frac{22 + 44 i + i + 2 (i^{1} i)}{(1 - 2 i) (1 + 2 i)}$

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

$\frac{22 + 44 i + i + 2 (i^{1} i^{1})}{(1 - 2 i) (1 + 2 i)}$

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

$\frac{22 + 44 i + i + 2 i^{1 + 1}}{(1 - 2 i) (1 + 2 i)}$

Add $1$ and $1$ .

$\frac{22 + 44 i + i + 2 i^{2}}{(1 - 2 i) (1 + 2 i)}$

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

$\frac{22 + 44 i + i + 2 \cdot - 1}{(1 - 2 i) (1 + 2 i)}$

Multiply $2$ by $- 1$ .

$\frac{22 + 44 i + i - 2}{(1 - 2 i) (1 + 2 i)}$

Subtract $2$ from $22$ .

$\frac{20 + 44 i + i}{(1 - 2 i) (1 + 2 i)}$

Add $44 i$ and $i$ .

$\frac{20 + 45 i}{(1 - 2 i) (1 + 2 i)}$

Simplify the denominator.

Expand $(1 - 2 i) (1 + 2 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{20 + 45 i}{1 (1 + 2 i) - 2 i (1 + 2 i)}$

Apply the distributive property.

$\frac{20 + 45 i}{1 \cdot 1 + 1 (2 i) - 2 i (1 + 2 i)}$

Apply the distributive property.

$\frac{20 + 45 i}{1 \cdot 1 + 1 (2 i) - 2 i \cdot 1 - 2 i (2 i)}$

Simplify.

Multiply $1$ by $1$ .

$\frac{20 + 45 i}{1 + 1 (2 i) - 2 i \cdot 1 - 2 i (2 i)}$

Multiply $2$ by $1$ .

$\frac{20 + 45 i}{1 + 2 i - 2 i \cdot 1 - 2 i (2 i)}$

Multiply $- 2$ by $1$ .

$\frac{20 + 45 i}{1 + 2 i - 2 i - 2 i (2 i)}$

Multiply $2$ by $- 2$ .

$\frac{20 + 45 i}{1 + 2 i - 2 i - 4 i i}$

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

$\frac{20 + 45 i}{1 + 2 i - 2 i - 4 (i^{1} i)}$

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

$\frac{20 + 45 i}{1 + 2 i - 2 i - 4 (i^{1} i^{1})}$

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

$\frac{20 + 45 i}{1 + 2 i - 2 i - 4 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{20 + 45 i}{1 + 2 i - 2 i - 4 i^{2}}$

Subtract $2 i$ from $2 i$ .

$\frac{20 + 45 i}{1 + 0 - 4 i^{2}}$

Add $1$ and $0$ .

$\frac{20 + 45 i}{1 - 4 i^{2}}$

Simplify each term.

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

$\frac{20 + 45 i}{1 - 4 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$\frac{20 + 45 i}{1 + 4}$

Add $1$ and $4$ .

$\frac{20 + 45 i}{5}$

Step 4

Cancel the common factor of $20 + 45 i$ and $5$ .

Factor $5$ out of $20$ .

$\frac{5 \cdot 4 + 45 i}{5}$

Factor $5$ out of $45 i$ .

$\frac{5 \cdot 4 + 5 (9 i)}{5}$

Factor $5$ out of $5 (4) + 5 (9 i)$ .

$\frac{5 (4 + 9 i)}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$\frac{5 (4 + 9 i)}{5 (1)}$

Cancel the common factor.

$\frac{5 (4 + 9 i)}{5 \cdot 1}$

Rewrite the expression.

$\frac{4 + 9 i}{1}$

Divide $4 + 9 i$ by $1$ .

$4 + 9 i$

Write in Standard Form (66+3i)/(3-6i)

Related Questions

Support LCMGCF.com by disabling your adblocker.