Algebra Examples

$(11 + i \sqrt{12}) - (- 8 + i \sqrt{3})$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $12$ .

$11 + i \sqrt{4 (3)} - (- 8 + i \sqrt{3})$

Step 1.1.2

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

$11 + i \sqrt{2^{2} \cdot 3} - (- 8 + i \sqrt{3})$

$11 + i \sqrt{2^{2} \cdot 3} - (- 8 + i \sqrt{3})$

Step 1.2

Pull terms out from under the radical.

$11 + i (2 \sqrt{3}) - (- 8 + i \sqrt{3})$

Step 1.3

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

$11 + 2 \cdot i \sqrt{3} - (- 8 + i \sqrt{3})$

Step 1.4

Apply the distributive property.

$11 + 2 i \sqrt{3} - - 8 - (i \sqrt{3})$

Step 1.5

Multiply $- 1$ by $- 8$ .

$11 + 2 i \sqrt{3} + 8 - i \sqrt{3}$

$11 + 2 i \sqrt{3} + 8 - i \sqrt{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $11$ and $8$ .

$2 i \sqrt{3} + 19 - i \sqrt{3}$

Step 2.2

Subtract $i \sqrt{3}$ from $2 i \sqrt{3}$ .

$1 i \sqrt{3} + 19$

Step 2.3

Simplify the expression.

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Step 2.3.1

Multiply $i$ by $1$ .

$i \sqrt{3} + 19$

Step 2.3.2

Reorder $i \sqrt{3}$ and $19$ .

$19 + i \sqrt{3}$

$19 + i \sqrt{3}$

$19 + i \sqrt{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$