Algebra Examples

$(7 \sqrt{- 1}) (3 \sqrt{- 4})$

Step 1

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

$7 i (3 \sqrt{- 4})$

Step 2

Rewrite $- 4$ as $- 1 (4)$ .

$7 i (3 \sqrt{- 1 (4)})$

Step 3

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$7 i (3 (\sqrt{- 1} \cdot \sqrt{4}))$

Step 4

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

$7 i (3 (i \cdot \sqrt{4}))$

Step 5

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

$7 i (3 (i \cdot \sqrt{2^{2}}))$

Step 6

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

$7 i (3 (i \cdot 2))$

Step 7

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

$7 i (3 (2 \cdot i))$

Step 8

Multiply $2$ by $3$ .

$7 i (6 i)$

Step 9

Multiply $7 i (6 i)$ .

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Step 9.1

Multiply $6$ by $7$ .

$42 i i$

Step 9.2

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

$42 (i^{1} i)$

Step 9.3

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

$42 (i^{1} i^{1})$

Step 9.4

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

$42 i^{1 + 1}$

Step 9.5

Add $1$ and $1$ .

$42 i^{2}$

Step 10

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

$42 \cdot - 1$

Step 11

Multiply $42$ by $- 1$ .

$- 42$