Trigonometry Examples

$f (x) = (x - 7 i) (x + 7 i)$

Step 1

Simplify $f (x)$ .

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Step 1.1

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

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Step 1.1.1

Apply the distributive property.

$f (x) = x (x + 7 i) - 7 i (x + 7 i)$

Step 1.1.2

Apply the distributive property.

$f (x) = x \cdot x + x (7 i) - 7 i (x + 7 i)$

Step 1.1.3

Apply the distributive property.

$f (x) = x \cdot x + x (7 i) - 7 i x - 7 i (7 i)$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the opposite terms in $x \cdot x + x (7 i) - 7 i x - 7 i (7 i)$ .

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Step 1.2.1.1

Reorder the factors in the terms $x (7 i)$ and $- 7 i x$ .

$f (x) = x \cdot x + 7 i x - 7 i x - 7 i (7 i)$

Step 1.2.1.2

Subtract $7 i x$ from $7 i x$ .

$f (x) = x \cdot x + 0 - 7 i (7 i)$

Step 1.2.1.3

Add $x \cdot x$ and $0$ .

$f (x) = x \cdot x - 7 i (7 i)$

Step 1.2.2

Simplify each term.

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Step 1.2.2.1

Multiply $x$ by $x$ .

$f (x) = x^{2} - 7 i (7 i)$

Step 1.2.2.2

Multiply $- 7 i (7 i)$ .

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Step 1.2.2.2.1

Multiply $7$ by $- 7$ .

$f (x) = x^{2} - 49 i i$

Step 1.2.2.2.2

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

$f (x) = x^{2} - 49 (i i)$

Step 1.2.2.2.3

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

$f (x) = x^{2} - 49 (i i)$

Step 1.2.2.2.4

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

$f (x) = x^{2} - 49 i^{1 + 1}$

Step 1.2.2.2.5

Add $1$ and $1$ .

$f (x) = x^{2} - 49 i^{2}$

Step 1.2.2.3

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

$f (x) = x^{2} - 49 \cdot - 1$

Step 1.2.2.4

Multiply $- 49$ by $- 1$ .

$f (x) = x^{2} + 49$

Step 2

The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be $0$ or $1$ . In this case, The degree of $f (x) = x^{2} + 49$ is $2$ , which makes the function a nonlinear function.

$f (x) = x^{2} + 49$ is not a linear function