Simplify 5/(3i-1)

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

Multiply the numerator and denominator of $\frac{5}{- 1 + 3 i}$ by the conjugate of $- 1 + 3 i$ to make the denominator real.

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

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $5$ by $- 1$ .

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

Multiply $- 3$ by $5$ .

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

Simplify the denominator.

Expand $(- 1 + 3 i) (- 1 - 3 i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify.

Multiply $- 1$ by $- 1$ .

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

Multiply $- 3$ by $- 1$ .

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

Multiply $- 1$ by $3$ .

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

Multiply $- 3$ by $3$ .

$\frac{- 5 - 15 i}{1 + 3 i - 3 i - 9 i i}$

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

$\frac{- 5 - 15 i}{1 + 3 i - 3 i - 9 (i^{1} i)}$

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

$\frac{- 5 - 15 i}{1 + 3 i - 3 i - 9 (i^{1} i^{1})}$

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

$\frac{- 5 - 15 i}{1 + 3 i - 3 i - 9 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 5 - 15 i}{1 + 3 i - 3 i - 9 i^{2}}$

Subtract $3 i$ from $3 i$ .

$\frac{- 5 - 15 i}{1 + 0 - 9 i^{2}}$

Add $1$ and $0$ .

$\frac{- 5 - 15 i}{1 - 9 i^{2}}$

Simplify each term.

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

$\frac{- 5 - 15 i}{1 - 9 \cdot - 1}$

Multiply $- 9$ by $- 1$ .

$\frac{- 5 - 15 i}{1 + 9}$

Add $1$ and $9$ .

$\frac{- 5 - 15 i}{10}$

Cancel the common factor of $- 5 - 15 i$ and $10$ .

Factor $5$ out of $- 5$ .

$\frac{5 (- 1) - 15 i}{10}$

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

$\frac{5 (- 1) + 5 (- 3 i)}{10}$

Factor $5$ out of $5 (- 1) + 5 (- 3 i)$ .

$\frac{5 (- 1 - 3 i)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{5 (- 1 - 3 i)}{5 \cdot 2}$

Cancel the common factor.

$\frac{5 (- 1 - 3 i)}{5 \cdot 2}$

Rewrite the expression.

$\frac{- 1 - 3 i}{2}$

Split the fraction $\frac{- 1 - 3 i}{2}$ into two fractions.

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

Simplify each term.

Move the negative in front of the fraction.

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

Move the negative in front of the fraction.

$- \frac{1}{2} - \frac{3 i}{2}$

Simplify 5/(3i-1)

Related Questions

Support LCMGCF.com by disabling your adblocker.