Algebra Examples

$\frac{7}{- 3 + \sqrt{- 2}}$

Step 1

Pull out imaginary unit $i$ .

Tap for more steps...

Step 1.1

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{7}{- 3 + \sqrt{- 1 (2)}}$

Step 1.2

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$\frac{7}{- 3 + \sqrt{- 1} \cdot \sqrt{2}}$

Step 1.3

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

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

Step 2

Multiply $\frac{7}{- 3 + i \cdot \sqrt{2}}$ by $\frac{- 3 - i \cdot \sqrt{2}}{- 3 - i \cdot \sqrt{2}}$ .

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

Step 3

Multiply $\frac{7}{- 3 + i \cdot \sqrt{2}}$ by $\frac{- 3 - i \cdot \sqrt{2}}{- 3 - i \cdot \sqrt{2}}$ .

$\frac{7 (- 3 - i \cdot \sqrt{2})}{(- 3 + i \cdot \sqrt{2}) (- 3 - i \cdot \sqrt{2})}$

Step 4

Expand the denominator using the FOIL method.

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

Step 5

Simplify.

$\frac{7 (- 3 - i \cdot \sqrt{2})}{11}$

Step 6

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{7 (- 1 (3) - i \sqrt{2})}{11}$

Step 7

Factor $- 1$ out of $- i \sqrt{2}$ .

$\frac{7 (- 1 (3) - (i \sqrt{2}))}{11}$

Step 8

Factor $- 1$ out of $- 1 (3) - (i \sqrt{2})$ .

$\frac{7 (- 1 (3 + i \sqrt{2}))}{11}$

Step 9

Move the negative in front of the fraction.

$- \frac{7 (3 + i \sqrt{2})}{11}$