https://file.aiquickdraw.com/mathbot/file/1727401400033y96v0qko.jpg

Here is the sketch of the locus of the point \( z \) described by the equation \( |z - 2| = 3 \). It represents a circle in the complex plane with:

- **Center**: \( (2, 0) \) (shown in red)
- **Radius**: 3 (the distance from the center to any point on the circle)

Feel free to ask for further details if needed. Here are some related questions:

1. How do you solve other types of modulus equations in the complex plane?
2. What is the general form of the equation for a circle in the complex plane?
3. How can this concept of locus be applied to real-world problems?
4. What happens if the center of the circle is a complex number instead of a real one?
5. How do transformations of the complex plane affect this kind of equation?

**Tip:** Modulus equations in the complex plane often represent geometric shapes such as lines or circles, depending on the structure of the equation.

This problem explains how to sketch the locus of a point defined by the equation |z - 2| = 3, representing a circle in the complex plane. Key concepts include complex modulus and the geometric representation of complex numbers. Suitable for students in Grades 9-12.

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