1. ## 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
$
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?

2. Hi,
Originally Posted by sazafraz
So how did we get the negative sign and the elimination of the i's?
The reason is that $i^2=-1$.

3. Originally Posted by flyingsquirrel
Hi,

The reason is that $i^2=-1$.
oh ok thank you, I didn't know that i is an imaginary unit