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- What are imaginary numbers? 21 answers
Can someone kind explain the mathematical quantity i to me (which is the square root of -1)?
Just to be clear, I'm not actually trying to understand i per se, I'm just trying to understand how it can possibly be defined as the square root of -1. I know that a square root is a number multiplied by itself to produce the original number e.g. 2 x 2 = 4. But I also recall that the only way a negative number can result from a multiplication is if exactly ONE of the two numbers is negative e.g. 2 x -2 = -4. But if the two numbers being multiplied are not the same magnitude and sign, then you are not actually squaring anything since a square root consists of a number of a given magnitude and sign multiplied by the exact same number with the exact same magnitude and sign. Therefore, it seems absurd to talk about the square root of a negative number.
I have never understood this and the teacher who taught us about i was never able to make it clear to me. It wouldn't surprise me if he didn't understand it himself.
I've wondered about this for many years now and never quite got around to tracking down a mathematician to explain it to me. I was wondering if anyone here could tackle this and help me understand?
I got pretty good marks in math right up until the end of high school - 40 years ago - but never did anything further in math at university or in my career. I'm just telling you that so you have some idea of who will be hearing your explanation.
I know that I learned about i in one of the three math classes I took in my final year of high school but I don't remember if it was algebra, calculus or geometry so I'm going to guess calculus. Please forgive me if I've tagged this incorrectly.