What are imaginary numbers?? Why can’t the square root of a negative be real?
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So there’s a number *i*, which is the square root of -1. In reality, there is no such number. There is no real number that you can multiply by itself (squaring it) and get a negative number. Any positive number squared is positive (2^2 = 4), and any *negative* number squared (-2^2 = 4) is also positive.
So, we just *pretend* there is a number that works that way, and we call that number *i*. The number *i* = √-1.
*i*^2 = -1
*i* is an imaginary number and any number you add or multiply *i* with is therefore also an imaginary number. They’re not “real” because they don’t exist on the number line. They’re not “real” because they don’t have a simple logical relationship with regular numbers. Like, for example, a real number is always greater than or less than another real number. 5 is greater than 4 but is less than 6.
But what about *i*? Is *i* greater than 5 or less than 5? It’s not really either, nor is it equal to it. This is because it is *imaginary*. It doesn’t play by the same rules that real numbers have to abide by.
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