Algebra Examples

$\frac{4}{\sqrt{- 4}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{4}{\sqrt{- 1 (4)}}$

Step 1.2

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$\frac{4}{\sqrt{- 1} \cdot \sqrt{4}}$

Step 1.3

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

$\frac{4}{i \cdot 2}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Move $2$ to the left of $i$ .

$\frac{4}{2 i}$

Step 3.2

Cancel the common factor of $4$ and $2$ .

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Step 3.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 2}{2 i}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $2 i$ .

$\frac{2 \cdot 2}{2 (i)}$

Step 3.2.2.2

Cancel the common factor.

$\frac{2 \cdot 2}{2 i}$

Step 3.2.2.3

Rewrite the expression.

$\frac{2}{i}$