Simplify (4+i)/(-9i)

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

Step 1

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

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

Step 2

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Reorder $4 i$ and $- 1$ .

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

Simplify the denominator.

Add parentheses.

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

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

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

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

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

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

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

Add $1$ and $1$ .

$\frac{- 1 + 4 i}{- 9 i^{2}}$

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

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

Step 3

Multiply $- 9$ by $- 1$ .

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

Step 4

Split the fraction $\frac{- 1 + 4 i}{9}$ into two fractions.

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

Step 5

Move the negative in front of the fraction.

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

Simplify (4+i)/(-9i)

Related Questions

Support LCMGCF.com by disabling your adblocker.