Basic Math Examples

$(- 2 - 1 i) \cdot (- 2 - 1 i)$

Step 1

Rewrite negatives.

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Step 1.1

Rewrite $- 1 i$ as $- i$ .

$(- 2 - i) \cdot (- 2 - 1 i)$

Step 1.2

Rewrite $- 1 i$ as $- i$ .

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

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

Step 2

Expand $(- 2 - i) (- 2 - i)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- 2 (- 2 - i) - i (- 2 - i)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $- 2$ by $- 2$ .

$4 - 2 (- i) - i \cdot - 2 - i (- i)$

Step 3.1.2

Multiply $- 1$ by $- 2$ .

$4 + 2 i - i \cdot - 2 - i (- i)$

Step 3.1.3

Multiply $- 2$ by $- 1$ .

$4 + 2 i + 2 i - i (- i)$

Step 3.1.4

Multiply $- i (- i)$ .

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Step 3.1.4.1

Multiply $- 1$ by $- 1$ .

$4 + 2 i + 2 i + 1 i i$

Step 3.1.4.2

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

$4 + 2 i + 2 i + 1 (i^{1} i)$

Step 3.1.4.3

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

$4 + 2 i + 2 i + 1 (i^{1} i^{1})$

Step 3.1.4.4

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

$4 + 2 i + 2 i + 1 i^{1 + 1}$

Step 3.1.4.5

Add $1$ and $1$ .

$4 + 2 i + 2 i + 1 i^{2}$

Step 3.1.4.6

Multiply $i^{2}$ by $1$ .

$4 + 2 i + 2 i + i^{2}$

$4 + 2 i + 2 i + i^{2}$

Step 3.1.5

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

$4 + 2 i + 2 i - 1$

$4 + 2 i + 2 i - 1$

Step 3.2

Subtract $1$ from $4$ .

$3 + 2 i + 2 i$

Step 3.3

Add $2 i$ and $2 i$ .

$3 + 4 i$

$3 + 4 i$

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