4) [20 points] Objective: Get a taste of the power of complex numbers for modeling more complex phenomena such as absorption. In many cases of interest, we end up solving a complex-valued Helmholtz equation of the form V2U(r)+ (k0 +1313)2 U(r) = 0 for real kc and g. a. Show that U (r) = A0 exp [i(k+i).r] is a solution to the complex Helmholtz equation, but requires a certain relationship between it , K, it , i} , and kg and Q. What is this relationship? [Note: These are an example of the inhomogeneous plane waves I mentioned briey in class. We'll see them show up later. ]