I want to ask for verification about whether this equation can be proven. If so, what is the best way to approach it? I tried this way... but I don't know how to continue on.
$$|B-Ae^{-j\omega\delta}|=|C-Ae^{+j\omega\delta}|$$ $$(B-Ae^{-j\omega\delta})(B^*-Ae^{+j\omega\delta})=(C-Ae^{+j\omega\delta})(C^*-Ae^{-j\omega\delta})$$ $$|B|^2-AB^*e^{-j\omega\delta}-ABe^{+j\omega\delta}+A^2 = |C|^2-AC^*e^{+j\omega\delta}-ACe^{-j\omega\delta}+A^2$$ $$|B|^2-2ARe\{B\times e^{+j\omega\delta}\}= |C|^2-2ARe\{C^*\times e^{+j\omega\delta}\}$$
given $B$ and $C$ are complex and $0<|A|\leq1 $.
Up to this point, I am stuck. I am not strong with math so I'm not sure how I can go about proving that $$B=C^*$$
Is it possible? Am I approaching the problem correctly? Any help will be much appreciated!