4 ms·

Video giving some intuition about e^(i•PI)=-1 https://www.youtube.com/watch?v=F_0yfvm0UoU https://www.youtube.com/watch?v=F_0yfvm0UoU

• thaumasiotes 8y ago
  The intuition is as simple as it gets; r·e^{iθ} is the complex number with radius r and angle θ. pi is just the angle that puts you on the negative half of the real number line. For why that identity holds, you do simple algebra on the non-simple Taylor series of those three functions (e^x, sin x, cos x). It is, to say the least, much less intuitive.
  • chrisweekly 8y ago
    The linked article mentions how helpful it is to have the right analogy (e.g. a number line, which you reference in your explanation of its intuitivenes). That's the main point: given the right analogy, things that otherwise seem arbitrary or nonsensical become clear and even intuitive. :)