What geometric shape in the complex plane is described by |z - (2 + 3i)| = 5?
Answer and explanation
Correct answer: C. A circle with center at (2, 3) and radius 5
- Step 1: The modulus |z - z0| represents Euclidean distance from z to the fixed point z0. Step 2. Setting distance equal to constant r = 5 defines a circle centered at z0 = 2 + 3i with radius 5. Answer: A circle with center at (2, 3) and radius 5. Why not the others: In Cartesian coordinates, this expands to (x - 2)^2 + (y - 3)^2 = 25.
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