Algebra Examples

$(5 + \sqrt{- 1}) (2 - \sqrt{- 36})$

Step 1

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

$(5 + i) (2 - \sqrt{- 36})$

Step 2

Rewrite $- 36$ as $- 1 (36)$ .

$(5 + i) (2 - \sqrt{- 1 (36)})$

Step 3

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$(5 + i) (2 - (\sqrt{- 1} \cdot \sqrt{36}))$

Step 4

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

$(5 + i) (2 - (i \cdot \sqrt{36}))$

Step 5

Simplify each term.

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Step 5.1

Rewrite $36$ as $6^{2}$ .

$(5 + i) (2 - (i \cdot \sqrt{6^{2}}))$

Step 5.2

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

$(5 + i) (2 - (i \cdot 6))$

Step 5.3

Move $6$ to the left of $i$ .

$(5 + i) (2 - (6 \cdot i))$

Step 5.4

Multiply $6$ by $- 1$ .

$(5 + i) (2 - 6 i)$

Step 6

Expand $(5 + i) (2 - 6 i)$ using the FOIL Method.

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Step 6.1

Apply the distributive property.

$5 (2 - 6 i) + i (2 - 6 i)$

Step 6.2

Apply the distributive property.

$5 \cdot 2 + 5 (- 6 i) + i (2 - 6 i)$

Step 6.3

Apply the distributive property.

$5 \cdot 2 + 5 (- 6 i) + i \cdot 2 + i (- 6 i)$

Step 7

Simplify and combine like terms.

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Step 7.1

Simplify each term.

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Step 7.1.1

Multiply $5$ by $2$ .

$10 + 5 (- 6 i) + i \cdot 2 + i (- 6 i)$

Step 7.1.2

Multiply $- 6$ by $5$ .

$10 - 30 i + i \cdot 2 + i (- 6 i)$

Step 7.1.3

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

$10 - 30 i + 2 \cdot i + i (- 6 i)$

Step 7.1.4

Multiply $i (- 6 i)$ .

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Step 7.1.4.1

Raise $i$ to the power of $1$ .

$10 - 30 i + 2 i - 6 (i^{1} i)$

Step 7.1.4.2

Raise $i$ to the power of $1$ .

$10 - 30 i + 2 i - 6 (i^{1} i^{1})$

Step 7.1.4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 - 30 i + 2 i - 6 i^{1 + 1}$

Step 7.1.4.4

Add $1$ and $1$ .

$10 - 30 i + 2 i - 6 i^{2}$

Step 7.1.5

Rewrite $i^{2}$ as $- 1$ .

$10 - 30 i + 2 i - 6 \cdot - 1$

Step 7.1.6

Multiply $- 6$ by $- 1$ .

$10 - 30 i + 2 i + 6$

Step 7.2

Add $10$ and $6$ .

$16 - 30 i + 2 i$

Step 7.3

Add $- 30 i$ and $2 i$ .

$16 - 28 i$