If z is a complex number such that $-\frac{\mathrm{\pi }}{2}\le \arg \mathrm{z}\le \frac{\mathrm{\pi }}{2}$, then which of the following inequalities is true?

• A

  $|\mathrm{z}-\overline{\mathrm{z}}|\le \left|\mathrm{z}\right|(\arg \mathrm{z}-\arg \overline{\mathrm{z}})$

• B

  $|\mathrm{z}-\overline{\mathrm{z}}|\ge \left|\mathrm{z}\right|(\arg \mathrm{z}-\arg \overline{\mathrm{z}})$

• C

  $|\mathrm{z}-\overline{\mathrm{z}}|<(\arg \mathrm{z}-\arg \overline{\mathrm{z}})$

• D

  None of these