Write in Standard Form (8+7i)/(3-4i)

$\frac{8 + 7 i}{3 - 4 i}$

Step 1

Multiply the numerator and denominator of $\frac{8 + 7 i}{3 - 4 i}$ by the conjugate of $3 - 4 i$ to make the denominator real.

$\frac{8 + 7 i}{3 - 4 i} \cdot \frac{3 + 4 i}{3 + 4 i}$

Step 2

Multiply.

Combine.

$\frac{(8 + 7 i) (3 + 4 i)}{(3 - 4 i) (3 + 4 i)}$

Simplify the numerator.

Expand $(8 + 7 i) (3 + 4 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{8 (3 + 4 i) + 7 i (3 + 4 i)}{(3 - 4 i) (3 + 4 i)}$

Apply the distributive property.

$\frac{8 \cdot 3 + 8 (4 i) + 7 i (3 + 4 i)}{(3 - 4 i) (3 + 4 i)}$

Apply the distributive property.

$\frac{8 \cdot 3 + 8 (4 i) + 7 i \cdot 3 + 7 i (4 i)}{(3 - 4 i) (3 + 4 i)}$

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $3$ .

$\frac{24 + 8 (4 i) + 7 i \cdot 3 + 7 i (4 i)}{(3 - 4 i) (3 + 4 i)}$

Multiply $4$ by $8$ .

$\frac{24 + 32 i + 7 i \cdot 3 + 7 i (4 i)}{(3 - 4 i) (3 + 4 i)}$

Multiply $3$ by $7$ .

$\frac{24 + 32 i + 21 i + 7 i (4 i)}{(3 - 4 i) (3 + 4 i)}$

Multiply $7 i (4 i)$ .

Multiply $4$ by $7$ .

$\frac{24 + 32 i + 21 i + 28 i i}{(3 - 4 i) (3 + 4 i)}$

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

$\frac{24 + 32 i + 21 i + 28 (i^{1} i)}{(3 - 4 i) (3 + 4 i)}$

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

$\frac{24 + 32 i + 21 i + 28 (i^{1} i^{1})}{(3 - 4 i) (3 + 4 i)}$

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

$\frac{24 + 32 i + 21 i + 28 i^{1 + 1}}{(3 - 4 i) (3 + 4 i)}$

Add $1$ and $1$ .

$\frac{24 + 32 i + 21 i + 28 i^{2}}{(3 - 4 i) (3 + 4 i)}$

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

$\frac{24 + 32 i + 21 i + 28 \cdot - 1}{(3 - 4 i) (3 + 4 i)}$

Multiply $28$ by $- 1$ .

$\frac{24 + 32 i + 21 i - 28}{(3 - 4 i) (3 + 4 i)}$

Subtract $28$ from $24$ .

$\frac{- 4 + 32 i + 21 i}{(3 - 4 i) (3 + 4 i)}$

Add $32 i$ and $21 i$ .

$\frac{- 4 + 53 i}{(3 - 4 i) (3 + 4 i)}$

Simplify the denominator.

Expand $(3 - 4 i) (3 + 4 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{- 4 + 53 i}{3 (3 + 4 i) - 4 i (3 + 4 i)}$

Apply the distributive property.

$\frac{- 4 + 53 i}{3 \cdot 3 + 3 (4 i) - 4 i (3 + 4 i)}$

Apply the distributive property.

$\frac{- 4 + 53 i}{3 \cdot 3 + 3 (4 i) - 4 i \cdot 3 - 4 i (4 i)}$

Simplify.

Multiply $3$ by $3$ .

$\frac{- 4 + 53 i}{9 + 3 (4 i) - 4 i \cdot 3 - 4 i (4 i)}$

Multiply $4$ by $3$ .

$\frac{- 4 + 53 i}{9 + 12 i - 4 i \cdot 3 - 4 i (4 i)}$

Multiply $3$ by $- 4$ .

$\frac{- 4 + 53 i}{9 + 12 i - 12 i - 4 i (4 i)}$

Multiply $4$ by $- 4$ .

$\frac{- 4 + 53 i}{9 + 12 i - 12 i - 16 i i}$

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

$\frac{- 4 + 53 i}{9 + 12 i - 12 i - 16 (i^{1} i)}$

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

$\frac{- 4 + 53 i}{9 + 12 i - 12 i - 16 (i^{1} i^{1})}$

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

$\frac{- 4 + 53 i}{9 + 12 i - 12 i - 16 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 4 + 53 i}{9 + 12 i - 12 i - 16 i^{2}}$

Subtract $12 i$ from $12 i$ .

$\frac{- 4 + 53 i}{9 + 0 - 16 i^{2}}$

Add $9$ and $0$ .

$\frac{- 4 + 53 i}{9 - 16 i^{2}}$

Simplify each term.

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

$\frac{- 4 + 53 i}{9 - 16 \cdot - 1}$

Multiply $- 16$ by $- 1$ .

$\frac{- 4 + 53 i}{9 + 16}$

Add $9$ and $16$ .

$\frac{- 4 + 53 i}{25}$

Step 3

Split the fraction $\frac{- 4 + 53 i}{25}$ into two fractions.

$\frac{- 4}{25} + \frac{53 i}{25}$

Step 4

Move the negative in front of the fraction.

$- \frac{4}{25} + \frac{53 i}{25}$

Write in Standard Form (8+7i)/(3-4i)

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