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Using the complex notation for waves can be a handy tool. Let E, = A, expli(k, .r-wit+6,)]+c.c. and Ez = A2expli(k2.r -wat + 62)] + c.c. be two interfering waves, where c.c. denotes the complex conjugate. (a) Calculate | E ? = EE* where E = E1 + E2. (b) Which terms of the above expression would be zero when time averaged over T, or Tz? (c) Rewrite | E|? as |E|? = f + g(t). Is it possible to choose T so that (g(t))r = 0 ? (d) Suppose now w = w1 = w2 and find I. Which terms are regarded as interference? Hints: Do not forget that A, and A2 are complex quantities! Euler's Identity : ex + 1 =0