Comments on: A Visual, Intuitive Guide to Imaginary Numbers https://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/ Math lessons that click Sun, 23 Aug 2026 16:50:43 +0000 hourly 1 By: blissful roses https://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/#comment-568432 Sun, 23 Aug 2026 16:50:43 +0000 http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/#comment-568432 this website is a godsend omg

]]> By: Waleed https://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/#comment-568356 Sat, 30 Nov 2024 15:07:14 +0000 http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/#comment-568356 I love your teaching style. So many people get scared away from science by bad teachers.

This is an excellent article.
In the spirit of maintaining the perfection of this article you might want to correct the typo in the following sentence from the article:
[We asked “How do we turn 1 into -1 in two steps?” and found an answer: rotate it 90 degrees...."]. Should be 180 degrees not 90 degrees.

Cheers, Waleed.

]]> By: Dimitris Tryfwnas https://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/#comment-568355 Thu, 28 Nov 2024 00:16:15 +0000 http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/#comment-568355 amazing explanation! thank you!

]]> By: Peter Harmon https://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/#comment-568284 Thu, 29 Jun 2023 05:22:00 +0000 http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/#comment-568284 I'm coming to this article very late. But I'd like to add something to your idea about people having a hard time dealing with negative numbers.
I think you yourself have probably heard that the first person to handle imaginary (and complex) numbers in a systematic and consistent way was the Italian Rafael Bombelli. But that was in 1572 when even negative numbers were considered strange things. And that's why Bombelli's view on this was completely different from the modern one. Not many people know this but it's actually useful to understand what he meant because then you'll have a better idea why he wrote certain things the way he did.
Bombelli himself didn't believe in negative numbers as autonomous objects. On the contrary, he did everything with positive numbers (i.e. absolute values) and what he suggested was 4 different operations of the lowest priority. He called them plus (this was ordinary addition), minus (this was ordinary subtraction), more than minus (this was equivalent to adding an imaginary quantity) and less than minus (which was equivalent to subtracting an imaginary quantity).
So the important thing for Bombelli was the fact that the result of an expression like "2 - 7" was not in the form of a number. The result of such an expression was another expression, namely "0 - 5". So for him, it was not a new number that would be called -5, it was a new expression of the form "0 - 5".
And that's why he then extended this idea further -- i.e. if we can add the number 5 or if we can subtract 5, we may also "more-than-subtract" 5 or we may "less-than-subtract" 5. But it's still the same positive number 5. So for Bombelli, a complex number like 2 + 5×i would be "2 >- 5" while 2 - 5×i would be "2 <- 5". And yet he was able to find cube roots with this!

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