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
= (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?