Where should the type information be 195

I don't think we really called that multiplying in the complex cases either. I think "expanding" might be a more accurate translation ... but anyone who figured out measuring angles in radians couldn't have missed that it's the same thing.

It's also "mathematically true" that you can count things in radians. After all, the radian is just an expanded form of 1 ;-)

For some years now, calculators with multiple-line input and proper precedence have been popular. Those gadgets can usually cope with this. Some even draw graphs for you.

The problem is that the kids then proceed to trust those calculators too far, and aren't capable of doing a sanity check on the results.

Well, it's just another computer. It probably has bugs and misfeatures and even if you don't hit any of those it's GIGO anyway, just like the rest of them. But the typical kid doesn't realize that about their home PC at that age either.

Heh. Reminds me of how we did that ... "They don't really cancel out but the difference isn't meaningful in this case, as that error margin is smaller than we can measure anyway" or "the mathematical representation of this isn't continuous but it works anyway because the border condition is outside the device's actual capabilities."

Yes, we essentially learned that too as a way to model certain kinds of circuits in electronics clbutt. Maths only got that far the following year.

Complex numbers were first officially introduced in the AC electronics clbutt, too. Was useful to many that you could see them on the scope.

-- #Not speaking for my employer. No warranty. YMMV.