Find the Complex Conjugate square root of -45

$\sqrt{- 45}$

Rewrite $- 45$ as $- 1 (45)$ .

$\sqrt{- 1 (45)}$

Rewrite $\sqrt{- 1 (45)}$ as $\sqrt{- 1} \cdot \sqrt{45}$ .

$\sqrt{- 1} \cdot \sqrt{45}$

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

$i \cdot \sqrt{45}$

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$i \cdot \sqrt{9 (5)}$

Rewrite $9$ as $3^{2}$ .

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

Pull terms out from under the radical.

$i \cdot (3 \sqrt{5})$

Move $3$ to the left of $i$ .

$3 i \sqrt{5}$

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

$- 3 i \sqrt{5}$