Precalculus Examples

$(8 + \sqrt{- 12}) - (4 + 2 \sqrt{3 i})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 12$ as $- 1 (12)$ .

$8 + \sqrt{- 1 (12)} - (4 + 2 \sqrt{3 i})$

Step 1.2

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$8 + \sqrt{- 1} \cdot \sqrt{12} - (4 + 2 \sqrt{3 i})$

Step 1.3

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

$8 + i \cdot \sqrt{12} - (4 + 2 \sqrt{3 i})$

Step 1.4

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 1.4.1

Factor $4$ out of $12$ .

$8 + i \cdot \sqrt{4 (3)} - (4 + 2 \sqrt{3 i})$

Step 1.4.2

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

$8 + i \cdot \sqrt{2^{2} \cdot 3} - (4 + 2 \sqrt{3 i})$

Step 1.5

Pull terms out from under the radical.

$8 + i \cdot (2 \sqrt{3}) - (4 + 2 \sqrt{3 i})$

Step 1.6

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

$8 + 2 \cdot i \sqrt{3} - (4 + 2 \sqrt{3 i})$

Step 1.7

Apply the distributive property.

$8 + 2 i \sqrt{3} - 1 \cdot 4 - (2 \sqrt{3 i})$

Step 1.8

Multiply $- 1$ by $4$ .

$8 + 2 i \sqrt{3} - 4 - (2 \sqrt{3 i})$

Step 1.9

Multiply $2$ by $- 1$ .

$8 + 2 i \sqrt{3} - 4 - 2 \sqrt{3 i}$

Step 2

Simplify the expression.

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Step 2.1

Subtract $4$ from $8$ .

$2 i \sqrt{3} + 4 - 2 \sqrt{3 i}$

Step 2.2

Reorder $2 i \sqrt{3}$ and $4$ .

$4 + 2 i \sqrt{3} - 2 \sqrt{3 i}$