Trigonometry Examples

$\frac{5}{\sqrt{- 16}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 16$ as $- 1 (16)$ .

$\frac{5}{\sqrt{- 1 (16)}}$

Step 1.2

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$\frac{5}{\sqrt{- 1} \cdot \sqrt{16}}$

Step 1.3

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

$\frac{5}{i \cdot \sqrt{16}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$\frac{5}{i \sqrt{4^{2}}}$

Step 2.2

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

$\frac{5}{i \cdot 4}$

Step 3

Move $4$ to the left of $i$ .

$\frac{5}{4 i}$