Question: What is the square root of -1?

Caspar Addyman answered on 14 Mar 2011:

There are two square roots of -1. One is called i and the other is -i. (Just like the two square roots of 1 are 1 and -1.) Obviously this number is a little strange because it’s not like the positive numbers and it’s not like the negative numbers. So people started calling these real numbers and called i and -i imaginary numbers. But in many ways imaginary numbers are no more or less strange or artificial than real numbers. Have you ever seen -1 apples? And what value exactly is pi? You can never really say because it goes on forever.

Despite being a bit weird, imaginary numbers work very much like real numbers. The square roots of 25 are 5 and -5.. and the square roots of -25 are 5i and -5i.. There isn’t any space for the imaginary numbers on the number line.. (the line that goes from minus infinity on the left straight through zero and off to plus infinity on the right) it is already full. But if you imagine another line crossing that at right angles, through zero and going off to minus imaginary infinity downwards and plus imaginary infinity upwards then that seems to make sense mathematically.

Now with two lines you suddenly have a whole plane of numbers that have one real value on the X-axis and one imaginary value on the Y-axis. Those are called complex numbers. But they aren’t much more complex. If you know a little bit of algebra you can easily work out how they work.