Simplify (4-3i)/(-4i)

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

Step 1

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

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

Step 2

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $- 3 i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

$\frac{4 i - 3 i^{2}}{- 4 i i}$

Simplify each term.

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

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

Multiply $- 3$ by $- 1$ .

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

Reorder $4 i$ and $3$ .

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

Simplify the denominator.

Add parentheses.

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

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

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

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

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

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

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

Add $1$ and $1$ .

$\frac{3 + 4 i}{- 4 i^{2}}$

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

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

Step 3

Multiply $- 4$ by $- 1$ .

$\frac{3 + 4 i}{4}$

Step 4

Split the fraction $\frac{3 + 4 i}{4}$ into two fractions.

$\frac{3}{4} + \frac{4 i}{4}$

Step 5

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3}{4} + \frac{4 i}{4}$

Divide $i$ by $1$ .

$\frac{3}{4} + i$

Simplify (4-3i)/(-4i)

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