Evaluate (-5+3i)/(15i)

$\frac{- 5 + 3 i}{15 i}$

Step 1

Multiply the numerator and denominator of $\frac{- 5 + 3 i}{15 i}$ by the conjugate of $15 i$ to make the denominator real.

$\frac{- 5 + 3 i}{15 i} \cdot \frac{i}{i}$

Step 2

Multiply.

Combine.

$\frac{(- 5 + 3 i) i}{15 i i}$

Simplify the numerator.

Apply the distributive property.

$\frac{- 5 i + 3 i i}{15 i i}$

Multiply $3 i i$ .

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

$\frac{- 5 i + 3 (i^{1} i)}{15 i i}$

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

$\frac{- 5 i + 3 (i^{1} i^{1})}{15 i i}$

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

$\frac{- 5 i + 3 i^{1 + 1}}{15 i i}$

Add $1$ and $1$ .

$\frac{- 5 i + 3 i^{2}}{15 i i}$

Simplify each term.

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

$\frac{- 5 i + 3 \cdot - 1}{15 i i}$

Multiply $3$ by $- 1$ .

$\frac{- 5 i - 3}{15 i i}$

Reorder $- 5 i$ and $- 3$ .

$\frac{- 3 - 5 i}{15 i i}$

Simplify the denominator.

Add parentheses.

$\frac{- 3 - 5 i}{15 (i i)}$

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

$\frac{- 3 - 5 i}{15 (i^{1} i)}$

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

$\frac{- 3 - 5 i}{15 (i^{1} i^{1})}$

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

$\frac{- 3 - 5 i}{15 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 3 - 5 i}{15 i^{2}}$

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

$\frac{- 3 - 5 i}{15 \cdot - 1}$

Step 3

Multiply $15$ by $- 1$ .

$\frac{- 3 - 5 i}{- 15}$

Step 4

Split the fraction $\frac{- 3 - 5 i}{- 15}$ into two fractions.

$\frac{- 3}{- 15} + \frac{- 5 i}{- 15}$

Step 5

Simplify each term.

Cancel the common factor of $- 3$ and $- 15$ .

Factor $- 3$ out of $- 3$ .

$\frac{- 3 (1)}{- 15} + \frac{- 5 i}{- 15}$

Cancel the common factors.

Factor $- 3$ out of $- 15$ .

$\frac{- 3 \cdot 1}{- 3 \cdot 5} + \frac{- 5 i}{- 15}$

Cancel the common factor.

$\frac{- 3 \cdot 1}{- 3 \cdot 5} + \frac{- 5 i}{- 15}$

Rewrite the expression.

$\frac{1}{5} + \frac{- 5 i}{- 15}$

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

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

$\frac{1}{5} + \frac{- 5 (i)}{- 15}$

Cancel the common factors.

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

$\frac{1}{5} + \frac{- 5 (i)}{- 5 (3)}$

Cancel the common factor.

$\frac{1}{5} + \frac{- 5 i}{- 5 \cdot 3}$

Rewrite the expression.

$\frac{1}{5} + \frac{i}{3}$

Evaluate (-5+3i)/(15i)

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