Algebra Examples

$(3 i + 5) + (6 + \sqrt{- 25})$

Step 1

Remove parentheses.

$3 i + 5 + 6 + \sqrt{- 25}$

Step 2

Simplify each term.

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Step 2.1

Rewrite $- 25$ as $- 1 (25)$ .

$3 i + 5 + 6 + \sqrt{- 1 (25)}$

Step 2.2

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$3 i + 5 + 6 + \sqrt{- 1} \cdot \sqrt{25}$

Step 2.3

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

$3 i + 5 + 6 + i \cdot \sqrt{25}$

Step 2.4

Rewrite $25$ as $5^{2}$ .

$3 i + 5 + 6 + i \cdot \sqrt{5^{2}}$

Step 2.5

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

$3 i + 5 + 6 + i \cdot 5$

Step 2.6

Move $5$ to the left of $i$ .

$3 i + 5 + 6 + 5 i$

Step 3

Simplify by adding terms.

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Step 3.1

Add $3 i$ and $5 i$ .

$5 + 6 + 8 i$

Step 3.2

Add $5$ and $6$ .

$11 + 8 i$