JEE Advance - Mathematics (1995 - No. 12)
If $$\left| {Z - W} \right| \le 1,\left| W \right| \le 1$$, show that $${\left| {Z - W} \right|^2} \le {(\left| Z \right| - \left| W \right|)^2} + {(ArgZ - Arg\,W)^2}$$
The inequality is always true.
The inequality holds only if Z and W are real numbers.
The inequality holds if Z and W are complex numbers with non-negative imaginary parts.
The inequality holds with the given conditions.
The inequality is false and counterexamples can be easily found.