Finite Math Examples

$(9 + 8 i) (9 + i)$

Step 1

Expand $(9 + 8 i) (9 + i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$9 (9 + i) + 8 i (9 + i)$

Step 1.2

Apply the distributive property.

$9 \cdot 9 + 9 i + 8 i (9 + i)$

Step 1.3

Apply the distributive property.

$9 \cdot 9 + 9 i + 8 i \cdot 9 + 8 i i$

$9 \cdot 9 + 9 i + 8 i \cdot 9 + 8 i i$

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 $9$ by $9$ .

$81 + 9 i + 8 i \cdot 9 + 8 i i$

Step 2.1.2

Multiply $9$ by $8$ .

$81 + 9 i + 72 i + 8 i i$

Step 2.1.3

Multiply $8 i i$ .

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Step 2.1.3.1

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

$81 + 9 i + 72 i + 8 (i^{1} i)$

Step 2.1.3.2

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

$81 + 9 i + 72 i + 8 (i^{1} i^{1})$

Step 2.1.3.3

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

$81 + 9 i + 72 i + 8 i^{1 + 1}$

Step 2.1.3.4

Add $1$ and $1$ .

$81 + 9 i + 72 i + 8 i^{2}$

$81 + 9 i + 72 i + 8 i^{2}$

Step 2.1.4

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

$81 + 9 i + 72 i + 8 \cdot - 1$

Step 2.1.5

Multiply $8$ by $- 1$ .

$81 + 9 i + 72 i - 8$

$81 + 9 i + 72 i - 8$

Step 2.2

Subtract $8$ from $81$ .

$73 + 9 i + 72 i$

Step 2.3

Add $9 i$ and $72 i$ .

$73 + 81 i$

$73 + 81 i$

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