Basic Math Examples

$\frac{9 + 7 \sqrt{- 9}}{2}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{9 + 7 \sqrt{- 1 (9)}}{2}$

Step 1.2

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$\frac{9 + 7 (\sqrt{- 1} \cdot \sqrt{9})}{2}$

Step 1.3

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

$\frac{9 + 7 (i \cdot \sqrt{9})}{2}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $9$ as $3^{2}$ .

$\frac{9 + 7 i \cdot \sqrt{3^{2}}}{2}$

Step 2.2

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

$\frac{9 + 7 i \cdot 3}{2}$

Step 2.3

Multiply $3$ by $7$ .

$\frac{9 + 21 i}{2}$