Question:
The region of the Argand plane defined by \( |z - 1| + |z + 1| \leq 4 \) is:
The region of the Argand plane defined by \( |z - 1| + |z + 1| \leq 4 \) is:
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In the Argand plane, the equation \( |z - a| + |z - b| = constant \) represents an ellipse.
Updated On: Jan 6, 2026
- Interior of an ellipse
- Exterior of a circle
- Interior and boundary of an ellipse
- Interior of a parabola
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The Correct Option is C
Solution and Explanation
Step 1: Recognize the equation.
The given equation represents the sum of distances from a point \( z \) to two fixed points, which is the general form of an ellipse.
Step 2: Conclusion. Thus, the region defined by this equation is the interior and boundary of an ellipse.
Step 2: Conclusion. Thus, the region defined by this equation is the interior and boundary of an ellipse.
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