Pre-Algebra Examples

${(2 - 7 i)}^{2}$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Rewrite ${(2 - 7 i)}^{2}$ as $(2 - 7 i) (2 - 7 i)$ .

$(2 - 7 i) (2 - 7 i)$

Step 1.2

Expand $(2 - 7 i) (2 - 7 i)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$2 (2 - 7 i) - 7 i (2 - 7 i)$

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $2$ by $2$ .

$4 + 2 (- 7 i) - 7 i \cdot 2 - 7 i (- 7 i)$

Step 1.3.1.2

Multiply $- 7$ by $2$ .

$4 - 14 i - 7 i \cdot 2 - 7 i (- 7 i)$

Step 1.3.1.3

Multiply $2$ by $- 7$ .

$4 - 14 i - 14 i - 7 i (- 7 i)$

Step 1.3.1.4

Multiply $- 7 i (- 7 i)$ .

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Step 1.3.1.4.1

Multiply $- 7$ by $- 7$ .

$4 - 14 i - 14 i + 49 i i$

Step 1.3.1.4.2

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

$4 - 14 i - 14 i + 49 (i^{1} i)$

Step 1.3.1.4.3

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

$4 - 14 i - 14 i + 49 (i^{1} i^{1})$

Step 1.3.1.4.4

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

$4 - 14 i - 14 i + 49 i^{1 + 1}$

Step 1.3.1.4.5

Add $1$ and $1$ .

$4 - 14 i - 14 i + 49 i^{2}$

Step 1.3.1.5

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

$4 - 14 i - 14 i + 49 \cdot - 1$

Step 1.3.1.6

Multiply $49$ by $- 1$ .

$4 - 14 i - 14 i - 49$

Step 1.3.2

Subtract $49$ from $4$ .

$- 45 - 14 i - 14 i$

Step 1.3.3

Subtract $14 i$ from $- 14 i$ .

$- 45 - 28 i$

Step 2

The degree cannot be determined because $- 45 - 28 i$ is not a polynomial.

Not a polynomial