Trigonometry Examples

$\frac{8 - \sqrt{- 36}}{10}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 36$ as $- 1 (36)$ .

$\frac{8 - \sqrt{- 1 (36)}}{10}$

Step 1.2

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$\frac{8 - (\sqrt{- 1} \cdot \sqrt{36})}{10}$

Step 1.3

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

$\frac{8 - (i \cdot \sqrt{36})}{10}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $36$ as $6^{2}$ .

$\frac{8 - i \cdot \sqrt{6^{2}}}{10}$

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{8 - i \cdot 6}{10}$

Step 2.3

Multiply $6$ by $- 1$ .

$\frac{8 - 6 i}{10}$

Step 3

Cancel the common factor of $8 - 6 i$ and $10$ .

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Step 3.1

Factor $2$ out of $8$ .

$\frac{2 (4) - 6 i}{10}$

Step 3.2

Factor $2$ out of $- 6 i$ .

$\frac{2 (4) + 2 (- 3 i)}{10}$

Step 3.3

Factor $2$ out of $2 (4) + 2 (- 3 i)$ .

$\frac{2 (4 - 3 i)}{10}$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $2$ out of $10$ .

$\frac{2 (4 - 3 i)}{2 \cdot 5}$

Step 3.4.2

Cancel the common factor.

$\frac{2 (4 - 3 i)}{2 \cdot 5}$

Step 3.4.3

Rewrite the expression.

$\frac{4 - 3 i}{5}$