Precalculus Examples

$(7 - i) (4 + 2 i)$

Step 1

Expand $(7 - i) (4 + 2 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 (4 + 2 i) - i (4 + 2 i)$

Step 1.2

Apply the distributive property.

$7 \cdot 4 + 7 (2 i) - i (4 + 2 i)$

Step 1.3

Apply the distributive property.

$7 \cdot 4 + 7 (2 i) - i \cdot 4 - i (2 i)$

$7 \cdot 4 + 7 (2 i) - i \cdot 4 - i (2 i)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $7$ by $4$ .

$28 + 7 (2 i) - i \cdot 4 - i (2 i)$

Step 2.1.2

Multiply $2$ by $7$ .

$28 + 14 i - i \cdot 4 - i (2 i)$

Step 2.1.3

Multiply $4$ by $- 1$ .

$28 + 14 i - 4 i - i (2 i)$

Step 2.1.4

Multiply $- i (2 i)$ .

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Step 2.1.4.1

Multiply $2$ by $- 1$ .

$28 + 14 i - 4 i - 2 i i$

Step 2.1.4.2

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

$28 + 14 i - 4 i - 2 (i^{1} i)$

Step 2.1.4.3

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

$28 + 14 i - 4 i - 2 (i^{1} i^{1})$

Step 2.1.4.4

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

$28 + 14 i - 4 i - 2 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$28 + 14 i - 4 i - 2 i^{2}$

$28 + 14 i - 4 i - 2 i^{2}$

Step 2.1.5

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

$28 + 14 i - 4 i - 2 \cdot - 1$

Step 2.1.6

Multiply $- 2$ by $- 1$ .

$28 + 14 i - 4 i + 2$

$28 + 14 i - 4 i + 2$

Step 2.2

Add $28$ and $2$ .

$30 + 14 i - 4 i$

Step 2.3

Subtract $4 i$ from $14 i$ .

$30 + 10 i$

$30 + 10 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$