Multiplying with q negative does genuinely correspond to a 180° rotation around the origin in the complex plane (plus a scalar multiplication of course)
I take your point, but honestly I’d bet many would be ready to learn about complex numbers a lot earlier if they were taught in this way.
Having such a memorable physical analogy “because I said so” is already miles better than the purely abstract “multiplying negatives makes a positive because I said so”, even if it still doesn’t mean you could teach extremely high level maths to six year olds.
Agreed. I’m trying to keep the reigns on an 11 year old, and we frequently talk both in what I would say is abstract. Also have to keep it somewhat grounded, because skipping multiple grades in math does not mean you will understand some things. Absolute value was an interesting conversation, and to be fair so was multiplying negatives.
Fun fact: exponents and multiplication DO work like rotation … in the complex domain (numbers with their imaginary component). It’s not a pure rotation unless it’s scalar, but it’s neat.
I know I explained that the worst ever, but 3blue1brown on YT talks about it and many other advanced math concepts in a lovely intuitive way.
Lmao not gonna lie, this would be a very intuitive way of teaching a kid negative values.
How is multiplying akin to rotating?
(-1)*(-1) = eiπ*eiπ = ei2π = 1
We’re looking for ELI5, not ELImathematician
Lol, yeah good luck explaining ‘e’ to a child who doesn’t understand basic multiplication.
Idk how they do it these days, but when I was a kid we learned the alphabet several years before multiplication. /j
Multiplying with q negative does genuinely correspond to a 180° rotation around the origin in the complex plane (plus a scalar multiplication of course)
Very intuitive to kids
I take your point, but honestly I’d bet many would be ready to learn about complex numbers a lot earlier if they were taught in this way.
Having such a memorable physical analogy “because I said so” is already miles better than the purely abstract “multiplying negatives makes a positive because I said so”, even if it still doesn’t mean you could teach extremely high level maths to six year olds.
Agreed. I’m trying to keep the reigns on an 11 year old, and we frequently talk both in what I would say is abstract. Also have to keep it somewhat grounded, because skipping multiple grades in math does not mean you will understand some things. Absolute value was an interesting conversation, and to be fair so was multiplying negatives.
Fun fact: exponents and multiplication DO work like rotation … in the complex domain (numbers with their imaginary component). It’s not a pure rotation unless it’s scalar, but it’s neat.
I know I explained that the worst ever, but 3blue1brown on YT talks about it and many other advanced math concepts in a lovely intuitive way.