Jewish World Review Jan. 4, 2006 / 4 Teves, 5766

Meet i

By Pat Sajak

http://www.JewishWorldReview.com | The time has long since passed when I could be of any use to my teenage son when it comes to the matter of math homework. I'm fairly useful in the fields of English and History, less so with Science and Latin, but totally superfluous in the bizarre world of Algebra.

That point was driven home again the other night when he introduced me to an imaginary number, or, as those wacky mathematicians like to call it, i. Here is the issue, as I understand it, and I'm not at all sure I do. There is no real way to find the square root of a negative number, because any number multiplied by itself would be positive. So, you might logically assume that, since a number can't exist, there's no point looking for it. Well, you'd be wrong. Apparently the inability of a number to exist isn't a sufficient reason not to find a way to pretend it exists.

Which brings us to i.

i is the square root of -1. (Or is it i am, the square root of -1?) And don't be fooled by the fact that there's no such thing as the square root of -1. Remember, we're talking about imaginary numbers, so just go with me on this. Now that we have a fake number, we can use it to make other fake numbers appear, well, real.

For example, there is no square root of -9. The number 3 doesn't work, because 3 times 3 equals a positive 9. Likewise, a negative 3 times a negative 3 nets a positive 9. But, hold on to your slide rules, because, thanks to i, we can now express the square root of negative 9 as the square root of negative 1 (that's our friend, i) times the square root of positive 9, which is i times 3, or 3i. In other words, the square root of -9 is 3i.

So, you see, we now have a way to express nonexistent numbers by using an imaginary number. You're probably asking yourself why we need imaginary numbers when things are tough enough when using real numbers. The truth is, I don't know. My son doesn't know, either. Neither his teacher nor his textbook explained why we do this other than because we're able to do it.

I'm sure there's a practical application for a number that's not really a number. Of course, it could be just an imaginary application. Perhaps it's a way to balance an overdrawn checking account or to measure the number of angels who can dance on the head of a pin.

So, as always, when it comes to Algebra, I'm out of the equation. Imagine that.