by stupidityismygam » Sun Mar 14, 2010 12:17 am
This is probably above UIL level, but not above UIL conceptually.
From De Moivre's we have that
[unparseable or potentially dangerous latex formula]
From the binomial theorem we know that
[unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula]
So, comparing real parts,
[unparseable or potentially dangerous latex formula]
Since, [unparseable or potentially dangerous latex formula] we have that [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]
Thus, we acquire the result
[unparseable or potentially dangerous latex formula]
We can find [unparseable or potentially dangerous latex formula] as well in a similar fashion and see that
[unparseable or potentially dangerous latex formula]
This gives us
[unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula]
Seeing this answer suggests that there is a pretty nifty generalization
my avatar is pretty awesome
tytia