# Euler's Formula

• Sep 7th 2008, 04:57 AM
sazafraz
Euler's Formula
I am having trouble understanding how somethign came up, I am sure it's something stupid that I just can't notice right now but I will ask anyway.

So to derive the cos (x+y) and sin(x+y) identities we write
\$\displaystyle
e^{ix}e^{iy}\$ = (cosx + isinx)(cosy +isiny)
= cosxcosy + isinxcosy + isinycosx - sinxsiny
= cosxcosy - sinxsiny + i(sinxcosy + sinycosx)

Therefore, cos(x+y) = cosxcosy - sinxsiny
sin(x+y) = sinxcosy + sinycosx
However, I do not understand the bolded part because I am thinking that (isinx)(isiny) would = isinxisiny. So how did we get the negative sign and the elimination of the i's?
• Sep 7th 2008, 05:09 AM
flyingsquirrel
Hi,
Quote:

Originally Posted by sazafraz
So how did we get the negative sign and the elimination of the i's?

The reason is that \$\displaystyle i^2=-1\$.
• Sep 7th 2008, 05:20 AM
sazafraz
Quote:

Originally Posted by flyingsquirrel
Hi,

The reason is that \$\displaystyle i^2=-1\$.

oh ok thank you, I didn't know that i is an imaginary unit