## Talk mathy to me: what’s the square root of i?

8 Apr 2013, 19:29 UTCMost people are probably aware that the square root of -1 isn’t a regular real number: it’s the imaginary number, which we often write as i. Of course, imaginary numbers aren’t any more “imaginary” than many other useful mathematical constructs; my feeling is that, if something in math can be used for something measurable, then [...]

A panel from “Saturday Morning Breakfast Cereal”. The comic behind the link is very NSFW and very nerdy, so don’t click if you’re offended by either. [Credit: Zach Weiner]Most people are probably aware that the square root of -1 isn’t a regular real number: it’s the imaginary number, which we often write as i. Of course, imaginary numbers aren’t any more “imaginary” than many other useful mathematical constructs; my feeling is that, if something in math can be used for something measurable, then it’s real in a meaningful sense.

People often ask the same question when they learn about imaginary numbers: if i is the square root of -1, what’s the square root of i? Is it a new kind of imaginary number, or can you write it in terms of “regular” imaginary numbers, or is it even a meaningful question? As you might ...