1. The inequality \(|z| \geq 2\) represents the region outside a circle centered at the origin with radius 2.

2. The inequality \(|z - 1 + i| \leq 1\) represents the region inside a circle centered at \(1 - i\) with radius 1.

3. On the Argand diagram, plot the circle centered at the origin with radius 2.

4. Plot the circle centered at \(1 - i\) with radius 1.

5. Shade the region that is outside the first circle and inside the second circle.