A shaded region on a complex plane is shown - HSC - SSCE Mathematics Extension 2 - Question 8 - 2023 - Paper 1

To investigate the relation that best describes the shaded region, we first need to analyze the inequality:

1. Understanding the context: The shaded region on the complex plane is likely a disk or area bounded by certain distances from the points $1$ and $i$ in the complex plane.

2. Analyzing the terms: The expression $|z - 1|$ represents the distance from the point $1$ while $|z - i|$ represents the distance from $i$. The inequality $|z - 1| < 2|z - i|$ suggests that points in the shaded region are closer to point $i$ than they are to point $1$.

3. Considering the locus of points: The geometrical interpretation of the inequality describes a region outside of an ellipse defined by the points $1$ and $2i$.

4. Conclusion: Thus, the best description for the shaded region is that it includes all $z$ such that the distance from $z$ to $1$ is less than twice the distance from $z$ to $i$. This matches option D: $|z - 1| < 2|z - i|$.