Thread: Maths!

Complex numbers

(cos(x)+isin(x))^n=cos(nx)+isin(nx)

Now using maclaurine series

e^ix=1+x+x^2/2!+x^3/3!+....+x^r/r!+...

this can be used to that

e^ix=cos(x)+isin(x)

which means

e^inx=cos(nx)+isin(nx)

this is then used to show that when n=1 x=pi

e^(ipi)=-1

e^(ipi)+1=0

This result has been describe by many as the most beautiful equation in Maths.

"Sniff, It's so... Beatutiful!!!"
:sobs:

It is pretty wonderful.

Oooh... try drawing f(x) = (-1)^x.

It always disturbed me that I couldn't really draw that one properly. Now I see that the plane of my graph paper was simply intersecting a line in a conceptual three dimensional space. Makes sense.

Originally Posted by Xei

Oooh... try drawing f(x) = (-1)^x.

How do you draw it?

I think he means graphing it on a line.