Simplify (12- square root of -81)/2

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

Pull out imaginary unit $i$ .

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

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

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

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

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

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

Simplify the numerator.

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

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

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

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

Move $9$ to the left of $i$ .

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

Multiply $9$ by $- 1$ .

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

Split the fraction $\frac{12 - 9 i}{2}$ into two fractions.

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

Simplify each term.

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Divide $12$ by $2$ .

$6 + \frac{- 9 i}{2}$

Move the negative in front of the fraction.

$6 - \frac{9 i}{2}$

Simplify (12- square root of -81)/2

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