Post by Admin on Feb 5, 2016 10:43:30 GMT
Imagine moving $\bar{P}$ up. $P$ will move down and the two regions will cross the real axis and overlap. The area of overlap will be symmetric about the real axis. Choose a point $a$ within this overlapping area. The three transformations are as follows
$$a\mapsto\bar{a}\mapsto [f(\bar{a})=(\text{rotation of }\phi)=\bar{a}e^{i\phi}]\mapsto ae^{-i\phi}$$
But this means that
$$f^{*}(a)=ae^{-i\phi}=(\text{rotation of }-\phi)$$
So $f(a)\neq f^{*}(a)$.
Vasco
$$a\mapsto\bar{a}\mapsto [f(\bar{a})=(\text{rotation of }\phi)=\bar{a}e^{i\phi}]\mapsto ae^{-i\phi}$$
But this means that
$$f^{*}(a)=ae^{-i\phi}=(\text{rotation of }-\phi)$$
So $f(a)\neq f^{*}(a)$.
Vasco