Question

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

• A. $|z-\overline{z}|\ge |z|(argz-arg\overline{z})$
• B. $|z-\overline{z}|\le |z|(argz-arg\overline{z})$
• C. $|z-\overline{z}|<(argz-arg\overline{z})$
• D. None of these

Answer 1

The correct option is B

$|z-\overline{z}|\le |z|(argz-arg\overline{z})$

$|z-\overline{z}|$ = straight line AB

While $|z|(argz-arg\overline{z})$ = Arc AB

$\therefore |z-\overline{z}|\le |z|(argz-arg\overline{z})$