Finite Math Examples

$| (- 4 - i) - 3 i (- 4 - i) |$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$| - 4 - i - 3 i \cdot - 4 - 3 i (- i) |$

Step 1.2

Multiply $- 4$ by $- 3$ .

$| - 4 - i + 12 i - 3 i (- i) |$

Step 1.3

Multiply $- 3 i (- i)$ .

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Step 1.3.1

Multiply $- 1$ by $- 3$ .

$| - 4 - i + 12 i + 3 i i |$

Step 1.3.2

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

$| - 4 - i + 12 i + 3 (i^{1} i) |$

Step 1.3.3

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

$| - 4 - i + 12 i + 3 (i^{1} i^{1}) |$

Step 1.3.4

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

$| - 4 - i + 12 i + 3 i^{1 + 1} |$

Step 1.3.5

Add $1$ and $1$ .

$| - 4 - i + 12 i + 3 i^{2} |$

Step 1.4

Simplify each term.

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Step 1.4.1

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

$| - 4 - i + 12 i + 3 \cdot - 1 |$

Step 1.4.2

Multiply $3$ by $- 1$ .

$| - 4 - i + 12 i - 3 |$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $3$ from $- 4$ .

$| - 7 - i + 12 i |$

Step 2.2

Add $- i$ and $12 i$ .

$| - 7 + 11 i |$

Step 3

Use the formula $| a + b i | = \sqrt{a^{2} + b^{2}}$ to find the magnitude.

$\sqrt{{(- 7)}^{2} + 11^{2}}$

Step 4

Raise $- 7$ to the power of $2$ .

$\sqrt{49 + 11^{2}}$

Step 5

Raise $11$ to the power of $2$ .

$\sqrt{49 + 121}$

Step 6

Add $49$ and $121$ .

$\sqrt{170}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt{170}$

Decimal Form:

$13.03840481 \dots$