Basic Math Examples

$6 - 12 i \div (- 3) - \sqrt{- 81}$

Step 1

Rewrite the division as a fraction.

$6 - \frac{12 i}{- 3} - \sqrt{- 81}$

Step 2

Cancel the common factor of $12$ and $- 3$ .

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Step 2.1

Factor $3$ out of $12 i$ .

$6 - \frac{3 (4 i)}{- 3} - \sqrt{- 81}$

Step 2.2

Move the negative one from the denominator of $\frac{4 i}{- 1}$ .

$6 - (- 1 \cdot (4 i)) - \sqrt{- 81}$

Step 3

Rewrite $- 1 \cdot (4 i)$ as $- (4 i)$ .

$6 - - (4 i) - \sqrt{- 81}$

Step 4

Multiply $4$ by $- 1$ .

$6 - (- 4 i) - \sqrt{- 81}$

Step 5

Multiply $- 4$ by $- 1$ .

$6 + 4 i - \sqrt{- 81}$

Step 6

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

$6 + 4 i - \sqrt{- 1 (81)}$

Step 7

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

$6 + 4 i - (\sqrt{- 1} \cdot \sqrt{81})$

Step 8

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

$6 + 4 i - (i \cdot \sqrt{81})$

Step 9

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

$6 + 4 i - (i \cdot \sqrt{9^{2}})$

Step 10

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

$6 + 4 i - (i \cdot 9)$

Step 11

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

$6 + 4 i - (9 i)$

Step 12

Multiply $9$ by $- 1$ .

$6 + 4 i - 9 i$

Step 13

Subtract $9 i$ from $4 i$ .

$6 - 5 i$