“NUMBERS of the form nsqrt{-1} are imaginary, but can still be used in equations.”^[1]
After seeing this, I was really stunned at what in the world that equation means.
Later, I found another weird equations through xkcd #217^[2].
I was really confused and I decided to find out what these equations mean and/or how they can be computed, really.
Especially, “e to the pi times i” was really hard to interpret.
I think a few of you already know about this thing, but for those like me, this might be really interesting.
The way ‘people’ calculate the value for “e to the pi times i” is… involving Taylor’s Series, which we are using these days in class.
In short, by Taylor’s Series, we can do the following by plugging in xi in place of x:

^[3]

The very last right side of the equation tells us that e^{pi i} = cospi + i sinpi = -1.
So, whatever it means that e has an imaginary power, the result is… an integer number!

If you find out this very interesting, there is another explanation to this using Calculus - see reference[3].

[1] http://xkcd.com/179/

[2] http://xkcd.com/217/

[3] http://www.math.toronto.edu/mathnet/questionCorner/epii.html