Playing with Euler's Equation

• Introducing Euler's Formula
• The exponential function is its own derivative
• A trick with derivatives of sin and cos
• Cos and Sin of the sum of angles

 OK now you can show:

which pretty much uses some of the most important numbers (each of the first three has a separate book written about it) and try this on for size - what is:

 

Imaginary raised to the imaginery? The answer lies here

Those books I mentioned earlier....

e - The Story of a Number by Eli Maor (Princeton Press)
An Imaginary Tale - The Story of i by Paul Nahim (Princeton Press)
A History of Pi by Peter Beckmann (Dorset)