Divide (9+16i)/(-4i)

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

Multiply the numerator and denominator of $\frac{9 + 16 i}{- 4 i}$ by the conjugate of $- 4 i$ to make the denominator real.

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

Multiply.

Combine.

$\frac{(9 + 16 i) i}{- 4 i i}$

Simplify the numerator.

Apply the distributive property.

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

Multiply $16 i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

Simplify each term.

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

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

Multiply $16$ by $- 1$ .

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

Reorder $9 i$ and $- 16$ .

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

Simplify the denominator.

Add parentheses.

$\frac{- 16 + 9 i}{- 4 (i i)}$

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $- 4$ by $- 1$ .

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

Split the fraction $\frac{- 16 + 9 i}{4}$ into two fractions.

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

Divide $- 16$ by $4$ .

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