The x-coordinate of the geometric centre of the graph is only half of the
story, it also has a y-coordinate as well, making it possible for us to plot
this 2 dimensional centre of mass onto a complex plain, which is always
elegant to do in maths when we deal with 2-dimensional information.
Now we can express the centre as a complex number, and the reason for
doing so is that complex numbers led themselves to nice descriptions of
things that have to do with rotating and rotation.
For example, Euler’s formula famously tells us that if
you take e to the power of some number times i, you
are going to land on the point you get, if you were to
walk that number of units around a circle with radius 1,
counter-clockwise starting from the right on the
complex plain (picture on the left).
So, imagine that you want to describe rotating at a rate
of one cycle per second, one thing you could do is that you can
time 2 pi since that is the circumference of the circle, and time
the power by t, the number of second passed to express the total
cycle passed. If you want to use this to describe a ration that has
some frequency, f, you can just simply time the power of e by f.
For example, if f = 0.1, then there will be a whole rotation after 10 seconds, since the time, t, must increase
to 10 before the full exponent looks like
2πi. The clockwise motion can be described as you add a minus sign in front.
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