Calculus Examples

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

Step 1

Multiply the numerator and denominator of $\frac{4 - 2 i}{i}$ by the conjugate of $i$ to make the denominator real.

$\frac{4 - 2 i}{i} \cdot \frac{i}{i}$

Step 2

Multiply.

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Step 2.1

Combine.

$\frac{(4 - 2 i) i}{i i}$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Apply the distributive property.

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

Step 2.2.2

Multiply $- 2 i i$ .

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Step 2.2.2.1

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

$\frac{4 i - 2 (i^{1} i)}{i i}$

Step 2.2.2.2

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

$\frac{4 i - 2 (i^{1} i^{1})}{i i}$

Step 2.2.2.3

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

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

Step 2.2.2.4

Add $1$ and $1$ .

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

Step 2.2.3

Simplify each term.

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Step 2.2.3.1

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

$\frac{4 i - 2 \cdot - 1}{i i}$

Step 2.2.3.2

Multiply $- 2$ by $- 1$ .

$\frac{4 i + 2}{i i}$

Step 2.2.4

Reorder $4 i$ and $2$ .

$\frac{2 + 4 i}{i i}$

Step 2.3

Simplify the denominator.

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Step 2.3.1

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

$\frac{2 + 4 i}{i^{1} i}$

Step 2.3.2

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

$\frac{2 + 4 i}{i^{1} i^{1}}$

Step 2.3.3

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

$\frac{2 + 4 i}{i^{1 + 1}}$

Step 2.3.4

Add $1$ and $1$ .

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

Step 2.3.5

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

$\frac{2 + 4 i}{- 1}$

Step 3

Move the negative one from the denominator of $\frac{2 + 4 i}{- 1}$ .

$- 1 \cdot (2 + 4 i)$

Step 4

Rewrite $- 1 \cdot (2 + 4 i)$ as $- (2 + 4 i)$ .

$- (2 + 4 i)$

Step 5

Apply the distributive property.

$- 1 \cdot 2 - (4 i)$

Step 6

Multiply $- 1$ by $2$ .

$- 2 - (4 i)$

Step 7

Multiply $4$ by $- 1$ .

$- 2 - 4 i$