Question 3 (6 points) 1. Let D C C be a subset and f: D C...

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Question 3 (6 points) 1. Let D C C be a subset and f: D C a function. Let zo D. Show that f is continuous at Zo if and only if (f) and I(f) are continuous at Zo. Here R(f) (resp. (f)) are the functions z R(f(z)) (resp. z I(f(z))). 2. Conclude that f: [a, b] C is continuous if and only if both f, f2: [a, b] R are continuous where f(x) = f(x) + i(x). Continuous functions such as f in 2. are also called paths in C. Question 3 (6 points) 1. Let D C C be a subset and f: D C a function. Let zo D. Show that f is continuous at Zo if and only if (f) and I(f) are continuous at Zo. Here R(f) (resp. (f)) are the functions z R(f(z)) (resp. z I(f(z))). 2. Conclude that f: [a, b] C is continuous if and only if both f, f2: [a, b] R are continuous where f(x) = f(x) + i(x). Continuous functions such as f in 2. are also called paths in C.