This might be a very obvious one, but I am stuck on this from a long time.
If $F(s) = M(s) + N(s)$ where $M(s)$ is even polynomial function and $N(s)$ is odd polynomial function (where $s$ is a complex number), then how do I prove that
${M(jw)}^2 - {N(jw)}^2 = {M(w)}^2 + {N(w)}^2$
where $j = (-1)^{1/2}$ and $w$ is real?
I am also now really confused as to what exactly is the definition of odd and even functions in the complex domain. Kindly help.
As experts say, this seems to be incorrect or atleast incomplete. However, I have taken this from a standard textbook on Network analysis and synthesis by F. F. Kuo. If this helps someone in finding the appropriate conditions under which this is true, kindly help. The book doesn't seem to indicate anything besides those I have mentioned. Thank you for the responses so far.