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.
I was already trying to visualize multiplying as a circle in my head and something clicks but cant grasp it.
Now reading that apparently
There is a real mathematical link i am dying to learn more. Do you know of an online visualizer/simulation that helps showing what you just said?
Honestly, the best online resource I know of are the 3blue1brown videos on complex numbers
Any tool risks confusing you more, since multiplying in the complex plane can act quite unexpectedly when you move outside the real line for both parameters
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.
I was already trying to visualize multiplying as a circle in my head and something clicks but cant grasp it.
Now reading that apparently There is a real mathematical link i am dying to learn more. Do you know of an online visualizer/simulation that helps showing what you just said?
Honestly, the best online resource I know of are the 3blue1brown videos on complex numbers
Any tool risks confusing you more, since multiplying in the complex plane can act quite unexpectedly when you move outside the real line for both parameters
Had a look around and this will quickly become one of my favorite media channels! Thanks!
Maybe this help https://www.nagwa.com/en/explainers/280109891548/
Or you can search Argand Diagram