Finite Math Examples

$9 + 3 i (7 - 2 i)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$9 + 3 i \cdot 7 + 3 i (- 2 i)$

Step 1.2

Multiply $7$ by $3$ .

$9 + 21 i + 3 i (- 2 i)$

Step 1.3

Multiply $3 i (- 2 i)$ .

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Step 1.3.1

Multiply $- 2$ by $3$ .

$9 + 21 i - 6 i i$

Step 1.3.2

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

$9 + 21 i - 6 (i^{1} i)$

Step 1.3.3

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

$9 + 21 i - 6 (i^{1} i^{1})$

Step 1.3.4

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

$9 + 21 i - 6 i^{1 + 1}$

Step 1.3.5

Add $1$ and $1$ .

$9 + 21 i - 6 i^{2}$

Step 1.4

Simplify each term.

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Step 1.4.1

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

$9 + 21 i - 6 \cdot - 1$

Step 1.4.2

Multiply $- 6$ by $- 1$ .

$9 + 21 i + 6$

Step 2

Add $9$ and $6$ .

$15 + 21 i$