> In the article <9610231009.AA20855email@example.com> > Dik.Winter@cwi.nl wrote: > > On Wed Oct 23 11:29:49 1996 Tleko wrote: > > > > z-z* = r.((cos@+isin@)-(cos(-@-pi)+isin(-@-pi))) > > > > = r.((cos@+isin@)-(-cos@ + isin@)) = 2 r cos@ > > > It should read : > > > z-z*=r.((cos@+isin@)-(cos(-@)+isin(-@-pi))) = 0. > > > On Mon 21 Oct 1996 23:24:01 Tleko wrote: > >> r.exp(i.(-@-pi)) = r.(cos(-@-pi)+i.sin(-@-pi)). > > > > Now, as z = r.exp(i.(-@-pi)) what is it? > > To derive the identity z=z* one must add pi only to the imaginary > value of z* to re-orient the axis y and write > > z* = r.(cos(-@)+isin(-@-pi)) > > to obtain z-z* = 0. Otherwise we would have z-z* = 2 r cos@ .
Which would be the correct result if one started from your (wrong) definition of z*. It's really crazy: to "prove" that common math is "faulty", you start by changing the definition of z*. As if that would not have been sufficient for rendering your argument moot, you use wrong trigonometric identities, and and explain that you have to use them in order to get a result inconsistent *both* with classical *and* your thwarted definitions.