4 ms·
Okay, this makes a little more sense to me, since it's just the power series again. But I don't think that calling a rotation a growth makes sense. Also, to me,
by jordigh 10y ago
Okay, this makes a little more sense to me, since it's just the power series again. But I don't think that calling a rotation a growth makes sense. Also, to me, the approximation e^(i epsilon) ~ 1 + i epsilon kind of begs the question.
- ThrustVectoring 10y agoe^(epsilon) ~ 1 + epsilon in general, because of the definition of the derivative and the fact that d/dx (e^x) = e^x
- jordigh 10y agoRight, the latter fact is equivalent to considering exp the solution of a differential equation, which is a much bigger fact. Treating the approximation as an innocent brute fact is what I considered begging the question, because why should this differential equation be valid for complex values?
- abecedarius 10y agoI was trying to make a geometric intuition accessible to high schoolers who haven't mastered calculus -- though I haven't tried it on an actual teenager. Of course there's also value in looking deeper into the foundations.