Here's the answer:


Think about the relationship: e^{ix }= cos x + i sin x now put in x = . (In geometry we us units of to measure angles instead of using degrees. The reason is that 360 degrees in a circle is a rather arbitrary number — why not 518 degrees, for example? Units of are more natural since the circumference of a circle whose radius is one is equal to 2, and units of are much easier to work with than degrees. As an angle, is the same as 180 degrees and 2 is 360 degrees.) And you'll get: e^{}^{ }= cos + i sin If you remember any high school trig, you'll see that the sine of is zero, so the imaginary term disappears, and the cosine of is 1. So you can write in one fell swoop: e^{}^{ }= 1 WOW!!! Who would have thought that if you raise the transcendental number e to an imaginary power of another transcendental number, you will get an integer!!!! And a negative one at that! OK, if you followed this, here's another question: What power of e added to 1 gives zero? Give up? Check here ==> ?

