Loci and regions of a complex number — A/L Combined Mathematics

How do I practise Loci and regions of a complex number?

1 question with a worked solution

Check before you answer: Boundary Inclusions: Using solid lines for non-strict inequalities (≤, ≥) and dashed lines for strict inequalities (<, >) with clear exclusion of origin points on rays.

1. In the complex plane, what geometric figure is described by the locus equation |z - (2 + 3i)| = 5?
   1. A) A straight line passing through (2, 3) with gradient 5
   2. B) A parabola with vertex at (2, 3)
   3. C) An ellipse with major axis 10
   4. D) A circle centered at (2, 3) with radius 5
   Check my answer

   Correct answer: D) A circle centered at (2, 3) with radius 5

   The equation |z - z₀| = r represents the locus of points z whose distance from the fixed point z₀ = 2 + 3i is constant and equal to 5. In Cartesian coordinates (x - 2)² + (y - 3)² = 5² = 25, which is a circle with center (2, 3) and radius 5.

   Show worked solution

   Step 1: Recognize standard locus: |z - z₀| = r is a circle centered at z₀ with radius r. Step 2: z₀ = 2 + 3i => Center = (2, 3); r = 5 => Radius = 5. Answer: A circle centered at (2, 3) with radius 5.
   Modelled on: the A/L Combined Mathematics examination pattern

Get this auto-marked

Next in the syllabus

Where does Loci and regions of a complex number fit in the syllabus?

Year 2 · Term 1