Question

If $|z + 1| < |z - 1|$, then $z$ lies:

• A. on the x-axis
• B. on the y-axis
• C. in the region $x < 0$
• D. in the region $y > 0$
• E. in the region $x > y$

Hint:

You can verify algebraically: \[ (x+1)^2 + y^2 < (x-1)^2 + y^2 \Rightarrow 4x < 0 \Rightarrow x < 0 \] Always remember: such inequalities divide the plane into two half-planes.

Answer 1

The Correct Option is C