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In my humble opinion, imaginary numbers are a core part of algebra, calculus, trigonometry, and physics, and all sufficiently intelligent people should learn ab
by lacker 5y ago
In my humble opinion, imaginary numbers are a core part of algebra, calculus, trigonometry, and physics, and all sufficiently intelligent people should learn about them. The reason exponential curves and sine waves show up all over the place in reality is because they are the solution to some simple differential equations. Imaginary numbers show you how these are fundamentally very similar things. Similarly, imaginary numbers make it clean and simple to solve cubic equations. And the idea that introducing this concept of "imaginary number" makes multiple practical applications much simpler, therefore we added it to mathematics, is core to how mathematics itself evolves.
- oneoff786 5y agoI’m willing to believe that. But I certainly never learned that. I only briefly got into differential equations by the end of high school. For our program imaginary numbers weren’t much more than learning some rules about how they work exponentially and an awkward introduction to vectors with complex numbers that really should have started with just real numbers. Maybe just teacher quality though. I can’t forget the frustration of both the class and our calc teacher when she realized our trig teacher from the prior year never conveyed the relationship between various trigonometric identities and the Pythagorean theorem and instantly made it vastly more intuitive.