Pre-Algebra Examples

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

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 - 2 i \cdot 3 - 2 i (2 i)$

Step 1.1.2

Multiply $3$ by $- 2$ .

$3 - 6 i - 2 i (2 i)$

Step 1.1.3

Multiply $- 2 i (2 i)$ .

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Step 1.1.3.1

Multiply $2$ by $- 2$ .

$3 - 6 i - 4 i i$

Step 1.1.3.2

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

$3 - 6 i - 4 (i^{1} i)$

Step 1.1.3.3

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

$3 - 6 i - 4 (i^{1} i^{1})$

Step 1.1.3.4

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

$3 - 6 i - 4 i^{1 + 1}$

Step 1.1.3.5

Add $1$ and $1$ .

$3 - 6 i - 4 i^{2}$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

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

$3 - 6 i - 4 \cdot - 1$

Step 1.1.4.2

Multiply $- 4$ by $- 1$ .

$3 - 6 i + 4$

Step 1.2

Add $3$ and $4$ .

$7 - 6 i$

Step 2

The degree cannot be determined because $7 - 6 i$ is not a polynomial.

Not a polynomial