Simplify (5+i)/(3i)

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

Step 1

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

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

Step 2

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Reorder $5 i$ and $- 1$ .

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

Simplify the denominator.

Add parentheses.

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

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

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

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

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

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

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

Add $1$ and $1$ .

$\frac{- 1 + 5 i}{3 i^{2}}$

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

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

Step 3

Multiply $3$ by $- 1$ .

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

Step 4

Split the fraction $\frac{- 1 + 5 i}{- 3}$ into two fractions.

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

Step 5

Simplify each term.

Dividing two negative values results in a positive value.

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

Move the negative in front of the fraction.

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

Simplify (5+i)/(3i)

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