Trigonometry Examples

$\sqrt{4 (- 1) - {(- 1)}^{2}}$

Step 1

Multiply $4$ by $- 1$ .

$\sqrt{- 4 - {(- 1)}^{2}}$

Step 2

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 2.1

Multiply $- 1$ by ${(- 1)}^{2}$ .

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Step 2.1.1

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

$\sqrt{- 4 + {(- 1)}^{1} {(- 1)}^{2}}$

Step 2.1.2

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

$\sqrt{- 4 + {(- 1)}^{1 + 2}}$

Step 2.2

Add $1$ and $2$ .

$\sqrt{- 4 + {(- 1)}^{3}}$

Step 3

Simplify the expression.

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Step 3.1

Raise $- 1$ to the power of $3$ .

$\sqrt{- 4 - 1}$

Step 3.2

Subtract $1$ from $- 4$ .

$\sqrt{- 5}$

Step 4

Rewrite $- 5$ as $- 1 (5)$ .

$\sqrt{- 1 (5)}$

Step 5

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$\sqrt{- 1} \cdot \sqrt{5}$

Step 6

Rewrite $\sqrt{- 1}$ as $i$ .

$i \sqrt{5}$