(a) Prove that (1) is equivalent to the pair of relations

(b)

(c)

(d) If f(z) is differentiable at z₀, show that f(z) is continuous at z₀.

(e) Show that f(z) = Re z = x is not differentiable at any z. Can you find other such functions?

(f) Show that f(z) = |z|² is differentiable only at z = 0; hence it is nowhere analytic.

Transcribed Image Text:

= Im I. lim Ref(z) = Re I, lim Im f(z) If lim f(x) exists, show that this limit is unique.