Finite Math Examples

$\frac{12 - \sqrt{- 81}}{2}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 81$ as $- 1 (81)$ .

$\frac{12 - \sqrt{- 1 (81)}}{2}$

Step 1.2

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$\frac{12 - (\sqrt{- 1} \cdot \sqrt{81})}{2}$

Step 1.3

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

$\frac{12 - (i \cdot \sqrt{81})}{2}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $81$ as $9^{2}$ .

$\frac{12 - i \cdot \sqrt{9^{2}}}{2}$

Step 2.2

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

$\frac{12 - i \cdot 9}{2}$

Step 2.3

Multiply $9$ by $- 1$ .

$\frac{12 - 9 i}{2}$