Precalculus Examples

$(- 7 - 9 i) (3 + i)$

Step 1

Expand $(- 7 - 9 i) (3 + i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$- 7 (3 + i) - 9 i (3 + i)$

Step 1.2

Apply the distributive property.

$- 7 \cdot 3 - 7 i - 9 i (3 + i)$

Step 1.3

Apply the distributive property.

$- 7 \cdot 3 - 7 i - 9 i \cdot 3 - 9 i i$

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 $3$ .

$- 21 - 7 i - 9 i \cdot 3 - 9 i i$

Step 2.1.2

Multiply $3$ by $- 9$ .

$- 21 - 7 i - 27 i - 9 i i$

Step 2.1.3

Multiply $- 9 i i$ .

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Step 2.1.3.1

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

$- 21 - 7 i - 27 i - 9 (i^{1} i)$

Step 2.1.3.2

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

$- 21 - 7 i - 27 i - 9 (i^{1} i^{1})$

Step 2.1.3.3

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

$- 21 - 7 i - 27 i - 9 i^{1 + 1}$

Step 2.1.3.4

Add $1$ and $1$ .

$- 21 - 7 i - 27 i - 9 i^{2}$

Step 2.1.4

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

$- 21 - 7 i - 27 i - 9 \cdot - 1$

Step 2.1.5

Multiply $- 9$ by $- 1$ .

$- 21 - 7 i - 27 i + 9$

Step 2.2

Add $- 21$ and $9$ .

$- 12 - 7 i - 27 i$

Step 2.3

Subtract $27 i$ from $- 7 i$ .

$- 12 - 34 i$