Evaluate (-10+ square root of -40)/2

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Algebra

$\frac{- 10 + \sqrt{- 40}}{2}$

Pull out imaginary unit $i$ .

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Rewrite $- 40$ as $- 1 (40)$ .

$\frac{- 10 + \sqrt{- 1 (40)}}{2}$

Rewrite $\sqrt{- 1 (40)}$ as $\sqrt{- 1} \cdot \sqrt{40}$ .

$\frac{- 10 + \sqrt{- 1} \cdot \sqrt{40}}{2}$

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

$\frac{- 10 + i \cdot \sqrt{40}}{2}$

Simplify the numerator.

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Rewrite $40$ as $2^{2} \cdot 10$ .

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Factor $4$ out of $40$ .

$\frac{- 10 + i \cdot \sqrt{4 (10)}}{2}$

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

$\frac{- 10 + i \cdot \sqrt{2^{2} \cdot 10}}{2}$

Pull terms out from under the radical.

$\frac{- 10 + i \cdot (2 \sqrt{10})}{2}$

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

$\frac{- 10 + 2 i \sqrt{10}}{2}$

Cancel the common factor of $- 10 + 2 i \sqrt{10}$ and $2$ .

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Factor $2$ out of $- 10$ .

$\frac{2 \cdot - 5 + 2 i \sqrt{10}}{2}$

Factor $2$ out of $2 i \sqrt{10}$ .

$\frac{2 \cdot - 5 + 2 (i \sqrt{10})}{2}$

Factor $2$ out of $2 (- 5) + 2 (i \sqrt{10})$ .

$\frac{2 (- 5 + i \sqrt{10})}{2}$

Cancel the common factors.

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Factor $2$ out of $2$ .

$\frac{2 (- 5 + i \sqrt{10})}{2 (1)}$

Cancel the common factor.

$\frac{2 (- 5 + i \sqrt{10})}{2 \cdot 1}$

Rewrite the expression.

$\frac{- 5 + i \sqrt{10}}{1}$

Divide $- 5 + i \sqrt{10}$ by $1$ .

$- 5 + i \sqrt{10}$

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