Algebra Examples

$(2 + \sqrt{- 1}) + (- 3 + \sqrt{- 16})$

Step 1

Remove parentheses.

$2 + \sqrt{- 1} - 3 + \sqrt{- 16}$

Step 2

Simplify each term.

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Step 2.1

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

$2 + i - 3 + \sqrt{- 16}$

Step 2.2

Rewrite $- 16$ as $- 1 (16)$ .

$2 + i - 3 + \sqrt{- 1 (16)}$

Step 2.3

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$2 + i - 3 + \sqrt{- 1} \cdot \sqrt{16}$

Step 2.4

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

$2 + i - 3 + i \cdot \sqrt{16}$

Step 2.5

Rewrite $16$ as $4^{2}$ .

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

Step 2.6

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

$2 + i - 3 + i \cdot 4$

Step 2.7

Move $4$ to the left of $i$ .

$2 + i - 3 + 4 i$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $3$ from $2$ .

$- 1 + i + 4 i$

Step 3.2

Add $i$ and $4 i$ .

$- 1 + 5 i$