Re: Help with confirmation on a small bit of assembly?

["John B. Matthews" <nospam@nospam.com>]

In article <KJKdnQUrfZMb4SPYnZ2dnUVZ_qyjnZ2d@comcast.com>,
 "Alex Freed" <alexf@mirrow.com> wrote:
> "Raymond Wiker" <raw@RawMBP.local> wrote in message 
> news:m2mz41sgz3.fsf@RawMBP.local...
> > "Michael J. Mahon" <mjmahon@aol.com> wrote:
> > >I've always considered the most beautiful math equation to be:
> > >
> > >   e^(2*i*pi) = -1
> > >
> > Not *completely* sure, but I think that's wrong... AFAIR, it
> > should be e^(pi*i) = -1...
> 
> Indeed
> 
> e^(z*i) = cos(z) + i*sin(z)
> sin(pi)=0
> cos(pi) = -1
> 
> -Alex.

Because sin(n*pi) is 0 everywhere and cos(n*pi) alternates between -1 
and 1 (n = 1, 2, ...), would it be correct to infer that

e^(n*i*pi) = -1 (odd n)
e^(n*i*pi) = +1 (even n)?

My favorite complex identity, analogous to the difference between two 
squares:

a^2 - b^2 = (a + b)(a - b),

is the sum of two squares:

a^2 + b^2 = (a + bi)(a - bi).

John
-- 
John Matthews
jmatthews at wright dot edu
www dot wright dot edu/~john.matthews/