Question

If $z$ is a complex number, then which of the following is not true .

• A. $z + \bar{z}$
• B. $z\bar{z}$
• C. $x$
• D. $y$

Answer 1

Answer: (C)

$x$

Answer 2

L.H.S.= $\because$

$z \neq \overline{z}$

$\left| z + \frac{2}{z} \right| = 2 \Rightarrow |z| - \frac{2}{|z|} \leq 2$ …..(i)

R.H.S. $|z|^{2} - 2|z| - 2 \leq 0$

$|z| \leq \frac{2 \pm \sqrt{4 + 8}}{2} \leq 1 \pm \sqrt{3}$ ……(ii)

Therefore $|z|$

(2) True (3) False (since $1 + \sqrt{3}$ ).