Write in Standard Form (4-3i)/(-1-4i)

$\frac{4 - 3 i}{- 1 - 4 i}$

Step 1

Multiply the numerator and denominator of $\frac{4 - 3 i}{- 1 - 4 i}$ by the conjugate of $- 1 - 4 i$ to make the denominator real.

$\frac{4 - 3 i}{- 1 - 4 i} \cdot \frac{- 1 + 4 i}{- 1 + 4 i}$

Step 2

Multiply.

Combine.

$\frac{(4 - 3 i) (- 1 + 4 i)}{(- 1 - 4 i) (- 1 + 4 i)}$

Simplify the numerator.

Expand $(4 - 3 i) (- 1 + 4 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{4 (- 1 + 4 i) - 3 i (- 1 + 4 i)}{(- 1 - 4 i) (- 1 + 4 i)}$

Apply the distributive property.

$\frac{4 \cdot - 1 + 4 (4 i) - 3 i (- 1 + 4 i)}{(- 1 - 4 i) (- 1 + 4 i)}$

Apply the distributive property.

$\frac{4 \cdot - 1 + 4 (4 i) - 3 i \cdot - 1 - 3 i (4 i)}{(- 1 - 4 i) (- 1 + 4 i)}$

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $- 1$ .

$\frac{- 4 + 4 (4 i) - 3 i \cdot - 1 - 3 i (4 i)}{(- 1 - 4 i) (- 1 + 4 i)}$

Multiply $4$ by $4$ .

$\frac{- 4 + 16 i - 3 i \cdot - 1 - 3 i (4 i)}{(- 1 - 4 i) (- 1 + 4 i)}$

Multiply $- 1$ by $- 3$ .

$\frac{- 4 + 16 i + 3 i - 3 i (4 i)}{(- 1 - 4 i) (- 1 + 4 i)}$

Multiply $- 3 i (4 i)$ .

Multiply $4$ by $- 3$ .

$\frac{- 4 + 16 i + 3 i - 12 i i}{(- 1 - 4 i) (- 1 + 4 i)}$

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

$\frac{- 4 + 16 i + 3 i - 12 (i^{1} i)}{(- 1 - 4 i) (- 1 + 4 i)}$

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

$\frac{- 4 + 16 i + 3 i - 12 (i^{1} i^{1})}{(- 1 - 4 i) (- 1 + 4 i)}$

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

$\frac{- 4 + 16 i + 3 i - 12 i^{1 + 1}}{(- 1 - 4 i) (- 1 + 4 i)}$

Add $1$ and $1$ .

$\frac{- 4 + 16 i + 3 i - 12 i^{2}}{(- 1 - 4 i) (- 1 + 4 i)}$

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

$\frac{- 4 + 16 i + 3 i - 12 \cdot - 1}{(- 1 - 4 i) (- 1 + 4 i)}$

Multiply $- 12$ by $- 1$ .

$\frac{- 4 + 16 i + 3 i + 12}{(- 1 - 4 i) (- 1 + 4 i)}$

Add $- 4$ and $12$ .

$\frac{8 + 16 i + 3 i}{(- 1 - 4 i) (- 1 + 4 i)}$

Add $16 i$ and $3 i$ .

$\frac{8 + 19 i}{(- 1 - 4 i) (- 1 + 4 i)}$

Simplify the denominator.

Expand $(- 1 - 4 i) (- 1 + 4 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{8 + 19 i}{- 1 (- 1 + 4 i) - 4 i (- 1 + 4 i)}$

Apply the distributive property.

$\frac{8 + 19 i}{- 1 \cdot - 1 - 1 (4 i) - 4 i (- 1 + 4 i)}$

Apply the distributive property.

$\frac{8 + 19 i}{- 1 \cdot - 1 - 1 (4 i) - 4 i \cdot - 1 - 4 i (4 i)}$

Simplify.

Multiply $- 1$ by $- 1$ .

$\frac{8 + 19 i}{1 - 1 (4 i) - 4 i \cdot - 1 - 4 i (4 i)}$

Multiply $4$ by $- 1$ .

$\frac{8 + 19 i}{1 - 4 i - 4 i \cdot - 1 - 4 i (4 i)}$

Multiply $- 1$ by $- 4$ .

$\frac{8 + 19 i}{1 - 4 i + 4 i - 4 i (4 i)}$

Multiply $4$ by $- 4$ .

$\frac{8 + 19 i}{1 - 4 i + 4 i - 16 i i}$

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

$\frac{8 + 19 i}{1 - 4 i + 4 i - 16 (i^{1} i)}$

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

$\frac{8 + 19 i}{1 - 4 i + 4 i - 16 (i^{1} i^{1})}$

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

$\frac{8 + 19 i}{1 - 4 i + 4 i - 16 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{8 + 19 i}{1 - 4 i + 4 i - 16 i^{2}}$

Add $- 4 i$ and $4 i$ .

$\frac{8 + 19 i}{1 + 0 - 16 i^{2}}$

Add $1$ and $0$ .

$\frac{8 + 19 i}{1 - 16 i^{2}}$

Simplify each term.

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

$\frac{8 + 19 i}{1 - 16 \cdot - 1}$

Multiply $- 16$ by $- 1$ .

$\frac{8 + 19 i}{1 + 16}$

Add $1$ and $16$ .

$\frac{8 + 19 i}{17}$

Step 3

Split the fraction $\frac{8 + 19 i}{17}$ into two fractions.

$\frac{8}{17} + \frac{19 i}{17}$

Write in Standard Form (4-3i)/(-1-4i)

Related Questions

Support LCMGCF.com by disabling your adblocker.