(4) (25%) In order to transmit a message to a receiver, the sender consumes energy Enx(d) = c d J/bit, where d is the Euclidean distance between the sender and the receiver, c is a constant, and a is a constant between 2 and 4 depending on the wireless environment. Assume that the energy consumption at the receiver is ignored. Given three nodes A, B, C placed at the vertexes of a triangle in a two-dimensional plane, A has two choices to send messages to C: one is that A sends messages directly to C, the other is that A sends messages to B and B relays the messages to C. Assume that di is the distance between A and B, d2 is the distance between B and C, d3 is the distance between A and C, and ZBAC =0. (4.1). Prove that the first choice consumes more energy than the second choice under the following conditions: (a) di d* cos(0), if a=2 (b) Xa -1> (1+X -2X*cos(0))a2 where X = d3/d, if 2