Algebra Examples

${(2 i)}^{2} \sqrt{\frac{- 1}{25}}$

Step 1

Apply the product rule to $2 i$ .

$2^{2} i^{2} \sqrt{\frac{- 1}{25}}$

Step 2

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

$4 i^{2} \sqrt{\frac{- 1}{25}}$

Step 3

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

$4 \cdot - 1 \sqrt{\frac{- 1}{25}}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $4$ by $- 1$ .

$- 4 \sqrt{\frac{- 1}{25}}$

Step 4.2

Move the negative in front of the fraction.

$- 4 \sqrt{- \frac{1}{25}}$

Step 5

Rewrite $- \frac{1}{25}$ as ${(\frac{i}{5})}^{2}$ .

$- 4 \sqrt{{(\frac{i}{5})}^{2}}$

Step 6

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

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

Step 7

Combine $- 4$ and $\frac{i}{5}$ .

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

Step 8

Move the negative in front of the fraction.

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