Precalculus Examples

$\frac{2 + \sqrt{- 25}}{4}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 25$ as $- 1 (25)$ .

$\frac{2 + \sqrt{- 1 (25)}}{4}$

Step 1.2

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$\frac{2 + \sqrt{- 1} \cdot \sqrt{25}}{4}$

Step 1.3

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

$\frac{2 + i \cdot \sqrt{25}}{4}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $25$ as $5^{2}$ .

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

Step 2.2

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

$\frac{2 + i \cdot 5}{4}$

Step 2.3

Move $5$ to the left of $i$ .

$\frac{2 + 5 i}{4}$