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I don't know why it stuck with me, but I still remember the concept of imaginary numbers.
Given that a square root of number is two equal numbers that when multiplied result in that number, and that a negative times a negative is a positive then -
-4 and +4 are both the square root of 16.
4i is the square root of -16. Since a negative number cannot really have a square root, but since it might occur in a formula, the square root of a negative number is an imaginary number (which is why it is marked 'i'). It can't exist but it has to be able to exist. It's sort of like mathematical antimatter.
If you consider that negative numbers themselves are a little fictitious (try fitting negative four apples into a bag), than imaginary numbers are just the result of extending the unrealistic into the absurd.
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