## anonymous 3 years ago How do you simplify numbers using the imaginary unit (i)? Ex: sqrt -16

1. AccessDenied

If you have something in the form $$\sqrt{-a}$$ for some $$a > 0$$, then we can break it up using exponent / radical properties: $$\sqrt{-a} = \sqrt{-1 \times a} = \sqrt{-1} \sqrt{a} = i \sqrt{a}$$

2. anonymous

so it would be i$\sqrt{16}$?

3. AccessDenied

$$i \sqrt{16}$$ Yes, although we can go a step further since $$\sqrt{16}$$ is the square root of a perfect square. = $$4i$$

4. anonymous

Okay thanks.

5. AccessDenied

You're welcome. :)