Complex Numbers And Quadratic Equations question 60
Question: The maximum value of $ |z| $ where z satisfies the condition $ | z+\frac{2}{z} |=2 $ is
Options:
A) $ \sqrt{3}-1 $
B) $ \sqrt{3}+1 $
C) $ \sqrt{3} $
D) $ \sqrt{2}+\sqrt{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ | z+\frac{2}{z} |=2\Rightarrow ||z|-\frac{2}{|z||}\le 2 $ Þ $ |z|^2 - 2|z| - 2 \le 0 $ $ |z| \le \frac{2\pm \sqrt{4+8}}{2} = 1\pm \sqrt{3} $ . Hence max. value of $ |z| $ is $ 1+\sqrt{3} $
BETA
