Question

The maximum value of | z | when z satisfies the condition $\left| z + \frac{2}{z} \right|$ = 2 is –

• A. $\sqrt{3}–1$
• B. $\sqrt{3} + 1$
• C. $\sqrt{2}$+ $\sqrt{3}$
• D. None of these

Answer 1

Answer: (B)

$\sqrt{3} + 1$

Answer 2

Sol. |\overset{̶}{Z}|– \frac{2}{|\overset{̶}{Z}|} £ \left| \overset{̶}{Z} + \frac{2}{\overset{̶}{Z}} \right| £|\overset{̶}{Z}|+ \frac{2}{|\overset{̶}{Z}|}

Ž|\overset{̶}{Z}| + \frac{2}{|\overset{̶}{Z}|}£ 2 £ |\overset{̶}{Z}|+ \frac{2}{|\overset{̶}{Z}|} Ž |\overset{̶}{Z}|^{2} – 2|\overset{̶}{Z}| – 2 £ 0

a.b =

$\frac{2 \pm \sqrt{4 + 8}}{2}$= 1 ± $\sqrt{3}$