in a sense there is an ‘order of operations’ error/overapplication of associative property here, where the student is working with (12+3) before addressing the “attached” i, and similarly with (2-3). In that case, I wouldn’t be surprised if the mistake was repeated to treat (12+3x) as (12+3)x. It would be interesting to give the student the same problem with x’s and see how they responded, but I’m also not totally sure about the distinction they would then make – i is not really a variable or an unknown, so if you addressed their error here by telling them to treat i like x, I expect in the next round you’d get 12+3i (=0), 3i = -12, i = -4.

Why don’t we just write complex numbers as bi+a? This would fix the whole problem, I am sure.

## 3 replies on “Adding Complex Numbers”

in a sense there is an ‘order of operations’ error/overapplication of associative property here, where the student is working with (12+3) before addressing the “attached” i, and similarly with (2-3). In that case, I wouldn’t be surprised if the mistake was repeated to treat (12+3x) as (12+3)x. It would be interesting to give the student the same problem with x’s and see how they responded, but I’m also not totally sure about the distinction they would then make – i is not really a variable or an unknown, so if you addressed their error here by telling them to treat i like x, I expect in the next round you’d get 12+3i (=0), 3i = -12, i = -4.

Why don’t we just write complex numbers as bi+a? This would fix the whole problem, I am sure.

Teach complex numbers through geometry first.