Algebra Examples

$i \sqrt{- 16}$

Step 1

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

$i \sqrt{- 1 (16)}$

Step 2

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

$i (\sqrt{- 1} \cdot \sqrt{16})$

Step 3

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

$i (i \cdot \sqrt{16})$

Step 4

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

$i (i \cdot \sqrt{4^{2}})$

Step 5

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

$i (i \cdot 4)$

Step 6

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

$i (4 \cdot i)$

Step 7

Multiply $i (4 i)$ .

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Step 7.1

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

$4 (i^{1} i)$

Step 7.2

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

$4 (i^{1} i^{1})$

Step 7.3

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

$4 i^{1 + 1}$

Step 7.4

Add $1$ and $1$ .

$4 i^{2}$

Step 8

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

$4 \cdot - 1$

Step 9

Multiply $4$ by $- 1$ .

$- 4$