20 October 2012

Department T-Shirt explained

Some of you might wonder about the equation on our department's T-shirt and I am here to explain.
Firstly you need to have some basic knowledge of complex numbers (that's the i) as well as exponents, the sin and cos functions and that pi (that is the π) is the ratio of a circles circumference to its diameter. (See: Picture).

This is the equation:
 
is the exponential function, hence it grows exponentially, i.e. very fast.

In complex numbers there is a formula called Euler's formula (which results from taking the Taylor series for cosy and siny), which is the following:
Now note that cos(π) = -1 and sin(π) = 0. Do you see it yet?
We just substitute y with π and then we get our equation.

Easy right?

Happy equating!

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