Simplify (i^2-16)/(i+4)

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

Multiply the numerator and denominator of $\frac{i^{2} - 16}{4 + 1 i}$ by the conjugate of $4 + 1 i$ to make the denominator real.

$\frac{i^{2} - 16}{4 + 1 i} \cdot \frac{4 - i}{4 - i}$

Multiply.

Combine.

$\frac{(i^{2} - 16) (4 - i)}{(4 + 1 i) (4 - i)}$

Simplify the numerator.

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

$\frac{(- 1 - 16) (4 - i)}{(4 + 1 i) (4 - i)}$

Subtract $16$ from $- 1$ .

$\frac{- 17 (4 - i)}{(4 + 1 i) (4 - i)}$

Apply the distributive property.

$\frac{- 17 \cdot 4 - 17 (- i)}{(4 + 1 i) (4 - i)}$

Multiply $- 17$ by $4$ .

$\frac{- 68 - 17 (- i)}{(4 + 1 i) (4 - i)}$

Multiply $- 1$ by $- 17$ .

$\frac{- 68 + 17 i}{(4 + 1 i) (4 - i)}$

Simplify the denominator.

Expand $(4 + 1 i) (4 - i)$ using the FOIL Method.

Apply the distributive property.

$\frac{- 68 + 17 i}{4 (4 - i) + 1 i (4 - i)}$

Apply the distributive property.

$\frac{- 68 + 17 i}{4 \cdot 4 + 4 (- i) + 1 i (4 - i)}$

Apply the distributive property.

$\frac{- 68 + 17 i}{4 \cdot 4 + 4 (- i) + 1 i \cdot 4 + 1 i (- i)}$

Simplify.

Multiply $4$ by $4$ .

$\frac{- 68 + 17 i}{16 + 4 (- i) + 1 i \cdot 4 + 1 i (- i)}$

Multiply $- 1$ by $4$ .

$\frac{- 68 + 17 i}{16 - 4 i + 1 i \cdot 4 + 1 i (- i)}$

Multiply $4$ by $1$ .

$\frac{- 68 + 17 i}{16 - 4 i + 4 i + 1 i (- i)}$

Multiply $- 1$ by $1$ .

$\frac{- 68 + 17 i}{16 - 4 i + 4 i - i i}$

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

$\frac{- 68 + 17 i}{16 - 4 i + 4 i - (i^{1} i)}$

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

$\frac{- 68 + 17 i}{16 - 4 i + 4 i - (i^{1} i^{1})}$

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

$\frac{- 68 + 17 i}{16 - 4 i + 4 i - i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 68 + 17 i}{16 - 4 i + 4 i - i^{2}}$

Add $- 4 i$ and $4 i$ .

$\frac{- 68 + 17 i}{16 + 0 - i^{2}}$

Add $16$ and $0$ .

$\frac{- 68 + 17 i}{16 - i^{2}}$

Simplify each term.

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

$\frac{- 68 + 17 i}{16 - - 1}$

Multiply $- 1$ by $- 1$ .

$\frac{- 68 + 17 i}{16 + 1}$

Add $16$ and $1$ .

$\frac{- 68 + 17 i}{17}$

Cancel the common factor of $- 68 + 17 i$ and $17$ .

Factor $17$ out of $- 68$ .

$\frac{17 \cdot - 4 + 17 i}{17}$

Factor $17$ out of $17 i$ .

$\frac{17 \cdot - 4 + 17 (i)}{17}$

Factor $17$ out of $17 (- 4) + 17 (i)$ .

$\frac{17 (- 4 + i)}{17}$

Cancel the common factors.

Factor $17$ out of $17$ .

$\frac{17 (- 4 + i)}{17 (1)}$

Cancel the common factor.

$\frac{17 (- 4 + i)}{17 \cdot 1}$

Rewrite the expression.

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

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

$- 4 + i$

Simplify (i^2-16)/(i+4)

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