Simplify (-35-15i)/(5i)

$\frac{- 35 - 15 i}{5 i}$

Step 1

Cancel the common factor of $- 35 - 15 i$ and $5$ .

Factor $5$ out of $- 35$ .

$\frac{5 \cdot - 7 - 15 i}{5 i}$

Factor $5$ out of $- 15 i$ .

$\frac{5 \cdot - 7 + 5 (- 3 i)}{5 i}$

Factor $5$ out of $5 (- 7) + 5 (- 3 i)$ .

$\frac{5 (- 7 - 3 i)}{5 i}$

Cancel the common factors.

Factor $5$ out of $5 i$ .

$\frac{5 (- 7 - 3 i)}{5 (i)}$

Cancel the common factor.

$\frac{5 (- 7 - 3 i)}{5 i}$

Rewrite the expression.

$\frac{- 7 - 3 i}{i}$

Step 2

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

$\frac{- 7 - 3 i}{i} \cdot \frac{i}{i}$

Step 3

Multiply.

Combine.

$\frac{(- 7 - 3 i) i}{i i}$

Simplify the numerator.

Apply the distributive property.

$\frac{- 7 i - 3 i i}{i i}$

Multiply $- 3 i i$ .

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

$\frac{- 7 i - 3 (i^{1} i)}{i i}$

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

$\frac{- 7 i - 3 (i^{1} i^{1})}{i i}$

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

$\frac{- 7 i - 3 i^{1 + 1}}{i i}$

Add $1$ and $1$ .

$\frac{- 7 i - 3 i^{2}}{i i}$

Simplify each term.

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

$\frac{- 7 i - 3 \cdot - 1}{i i}$

Multiply $- 3$ by $- 1$ .

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

Reorder $- 7 i$ and $3$ .

$\frac{3 - 7 i}{i i}$

Simplify the denominator.

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

$\frac{3 - 7 i}{i^{1} i}$

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

$\frac{3 - 7 i}{i^{1} i^{1}}$

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

$\frac{3 - 7 i}{i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{3 - 7 i}{i^{2}}$

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

$\frac{3 - 7 i}{- 1}$

Step 4

Simplify the expression.

Move the negative one from the denominator of $\frac{3 - 7 i}{- 1}$ .

$- 1 \cdot (3 - 7 i)$

Rewrite $- 1 \cdot (3 - 7 i)$ as $- (3 - 7 i)$ .

$- (3 - 7 i)$

Step 5

Apply the distributive property.

$- 1 \cdot 3 - (- 7 i)$

Step 6

Multiply.

Multiply $- 1$ by $3$ .

$- 3 - (- 7 i)$

Multiply $- 7$ by $- 1$ .

$- 3 + 7 i$

Simplify (-35-15i)/(5i)

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