Proof () Let us suppose that { 1. }  By definition, given , there exists > 0 :

0 < { 2. }    |u(x, y) - u₀ + i(v(x, y) - v₀)| < .

We deduce that   { 3. }, 0 < |y - y₀| < /2     |u(x, y ) - u₀| < ,   { 4. }.

This completes this part of the proof.

Match the above boxes 1, 2, 3, 4 with the selections:

(a) |v(x, y) - v₀| <   (b) |x - x₀ + i(y - y₀)| <   (c) (d) 0 < |x - x₀| < /2

My solutions: