Pre-Algebra Examples

$(7 + 5 i) (- 6 + 9 i)$

Step 1

Expand $(7 + 5 i) (- 6 + 9 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 (- 6 + 9 i) + 5 i (- 6 + 9 i)$

Step 1.2

Apply the distributive property.

$7 \cdot - 6 + 7 (9 i) + 5 i (- 6 + 9 i)$

Step 1.3

Apply the distributive property.

$7 \cdot - 6 + 7 (9 i) + 5 i \cdot - 6 + 5 i (9 i)$

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 $- 6$ .

$- 42 + 7 (9 i) + 5 i \cdot - 6 + 5 i (9 i)$

Step 2.1.2

Multiply $9$ by $7$ .

$- 42 + 63 i + 5 i \cdot - 6 + 5 i (9 i)$

Step 2.1.3

Multiply $- 6$ by $5$ .

$- 42 + 63 i - 30 i + 5 i (9 i)$

Step 2.1.4

Multiply $5 i (9 i)$ .

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Step 2.1.4.1

Multiply $9$ by $5$ .

$- 42 + 63 i - 30 i + 45 i i$

Step 2.1.4.2

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

$- 42 + 63 i - 30 i + 45 (i^{1} i)$

Step 2.1.4.3

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

$- 42 + 63 i - 30 i + 45 (i^{1} i^{1})$

Step 2.1.4.4

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

$- 42 + 63 i - 30 i + 45 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$- 42 + 63 i - 30 i + 45 i^{2}$

Step 2.1.5

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

$- 42 + 63 i - 30 i + 45 \cdot - 1$

Step 2.1.6

Multiply $45$ by $- 1$ .

$- 42 + 63 i - 30 i - 45$

Step 2.2

Subtract $45$ from $- 42$ .

$- 87 + 63 i - 30 i$

Step 2.3

Subtract $30 i$ from $63 i$ .

$- 87 + 33 i$