Yep, you heard us right. We know what you’re thinking: “But wait, isn’t a square root always positive or zero?”

First off, let’s clarify that we’re not talking about the real numbers here (sorry, math purists). Instead, we’re diving into the world of complex numbers those ***** little guys with an imaginary component. And when it comes to square roots in this realm, things get a bit… interesting.

So how do you calculate the square root of a negative number? Well, let’s take our trusty example: (-16). If we were dealing with real numbers, we would simply say that there is no such thing as the square root of -16 (because it doesn’t exist in this realm). But when we move into complex land, things get a bit more… creative.

To find the square root of (-16), you might be tempted to take the square root of 16 and then multiply by -1. However, that won’t work because taking the square root of a positive number always gives us a positive result (unless we’re dealing with zero). So what do we do?

Well, here’s where things get funky: instead of using real numbers to calculate our answer, we use complex numbers. And when it comes to calculating the square root of (-16), that means taking the square root of 16 and then multiplying by -i (where i is the imaginary unit).

So what does this look like in practice? Let’s break it down:

(-16) = (-4 * 4)

To find the square root, we take the square root of each term inside the parentheses. That gives us:

sqrt(-16) = sqrt(-4) * sqrt(4)

Now let’s deal with those ***** negative signs. To get rid of them, we use a little trick called “conjugation”. This involves multiplying our answer by the complex conjugate (which is simply the same number but with the opposite sign for the imaginary component). So in this case:

sqrt(-16) = sqrt(-4) * sqrt(4)

i
—–
-4 * i

To get rid of those negative signs, we multiply by their conjugates (which are simply the same number but with opposite imaginary components):

sqrt(-16) = (-2 + 0i) * (-2 0i) / (-2 0i) * (-2 + 0i)

i
—–
-4 * i

The square root of a negative number in complex land. It might not be what we’re used to, but it sure is funky. So next time someone asks you for the square root of (-16), just remember: don’t panic, and always keep an open mind (and maybe a calculator handy).