Find the Complex Conjugate square root of -100

$\sqrt{- 100}$

Step 1

Rewrite $- 100$ as $- 1 (100)$ .

$\sqrt{- 1 (100)}$

Step 2

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$\sqrt{- 1} \cdot \sqrt{100}$

Step 3

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

$i \cdot \sqrt{100}$

Step 4

Rewrite $100$ as $10^{2}$ .

$i \cdot \sqrt{10^{2}}$

Step 5

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

$i \cdot 10$

Step 6

Move $10$ to the left of $i$ .

$10 i$

Step 7

To find the complex conjugate, negate the term with $i$ .

$- 10 i$