Write in Standard Form (9i)/(8+8i)

$\frac{9 i}{8 + 8 i}$

Step 1

Multiply the numerator and denominator of $\frac{9 i}{8 + 8 i}$ by the conjugate of $8 + 8 i$ to make the denominator real.

$\frac{9 i}{8 + 8 i} \cdot \frac{8 - 8 i}{8 - 8 i}$

Step 2

Multiply.

Combine.

$\frac{9 i (8 - 8 i)}{(8 + 8 i) (8 - 8 i)}$

Simplify the numerator.

Apply the distributive property.

$\frac{9 i \cdot 8 + 9 i (- 8 i)}{(8 + 8 i) (8 - 8 i)}$

Multiply $8$ by $9$ .

$\frac{72 i + 9 i (- 8 i)}{(8 + 8 i) (8 - 8 i)}$

Multiply $9 i (- 8 i)$ .

Multiply $- 8$ by $9$ .

$\frac{72 i - 72 i i}{(8 + 8 i) (8 - 8 i)}$

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

$\frac{72 i - 72 (i^{1} i)}{(8 + 8 i) (8 - 8 i)}$

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

$\frac{72 i - 72 (i^{1} i^{1})}{(8 + 8 i) (8 - 8 i)}$

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

$\frac{72 i - 72 i^{1 + 1}}{(8 + 8 i) (8 - 8 i)}$

Add $1$ and $1$ .

$\frac{72 i - 72 i^{2}}{(8 + 8 i) (8 - 8 i)}$

Simplify each term.

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

$\frac{72 i - 72 \cdot - 1}{(8 + 8 i) (8 - 8 i)}$

Multiply $- 72$ by $- 1$ .

$\frac{72 i + 72}{(8 + 8 i) (8 - 8 i)}$

Reorder $72 i$ and $72$ .

$\frac{72 + 72 i}{(8 + 8 i) (8 - 8 i)}$

Simplify the denominator.

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

Apply the distributive property.

$\frac{72 + 72 i}{8 (8 - 8 i) + 8 i (8 - 8 i)}$

Apply the distributive property.

$\frac{72 + 72 i}{8 \cdot 8 + 8 (- 8 i) + 8 i (8 - 8 i)}$

Apply the distributive property.

$\frac{72 + 72 i}{8 \cdot 8 + 8 (- 8 i) + 8 i \cdot 8 + 8 i (- 8 i)}$

Simplify.

Multiply $8$ by $8$ .

$\frac{72 + 72 i}{64 + 8 (- 8 i) + 8 i \cdot 8 + 8 i (- 8 i)}$

Multiply $- 8$ by $8$ .

$\frac{72 + 72 i}{64 - 64 i + 8 i \cdot 8 + 8 i (- 8 i)}$

Multiply $8$ by $8$ .

$\frac{72 + 72 i}{64 - 64 i + 64 i + 8 i (- 8 i)}$

Multiply $- 8$ by $8$ .

$\frac{72 + 72 i}{64 - 64 i + 64 i - 64 i i}$

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

$\frac{72 + 72 i}{64 - 64 i + 64 i - 64 (i^{1} i)}$

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

$\frac{72 + 72 i}{64 - 64 i + 64 i - 64 (i^{1} i^{1})}$

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

$\frac{72 + 72 i}{64 - 64 i + 64 i - 64 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{72 + 72 i}{64 - 64 i + 64 i - 64 i^{2}}$

Add $- 64 i$ and $64 i$ .

$\frac{72 + 72 i}{64 + 0 - 64 i^{2}}$

Add $64$ and $0$ .

$\frac{72 + 72 i}{64 - 64 i^{2}}$

Simplify each term.

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

$\frac{72 + 72 i}{64 - 64 \cdot - 1}$

Multiply $- 64$ by $- 1$ .

$\frac{72 + 72 i}{64 + 64}$

Add $64$ and $64$ .

$\frac{72 + 72 i}{128}$

Step 3

Cancel the common factor of $72 + 72 i$ and $128$ .

Factor $8$ out of $72$ .

$\frac{8 (9) + 72 i}{128}$

Factor $8$ out of $72 i$ .

$\frac{8 (9) + 8 (9 i)}{128}$

Factor $8$ out of $8 (9) + 8 (9 i)$ .

$\frac{8 (9 + 9 i)}{128}$

Cancel the common factors.

Factor $8$ out of $128$ .

$\frac{8 (9 + 9 i)}{8 \cdot 16}$

Cancel the common factor.

$\frac{8 (9 + 9 i)}{8 \cdot 16}$

Rewrite the expression.

$\frac{9 + 9 i}{16}$

Step 4

Split the fraction $\frac{9 + 9 i}{16}$ into two fractions.

$\frac{9}{16} + \frac{9 i}{16}$

Write in Standard Form (9i)/(8+8i)

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