Complex Numbers
Locus
Premium Question
Grade 11
Question:
The locus of $z$ satisfying $|z - 1| \leq |z + 1|$ is:
(1) $\operatorname{Re}(z) \leq 0$
(2) $\operatorname{Re}(z) \geq 0$
(3) $|z| \leq 1$
(4) $\operatorname{Im}(z) \geq 0$
Step-by-Step Solution
Key Concept: Square both sides and write $z = x + iy$. The condition $|z - 1|^2 \leq |z + 1|^2$ simplifies to a linear inequality in $x$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)