The maximum value of |z| when z satisfies the condition |z+2z| =2 is

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3−1

3+1

2 +3

answer is B.

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Detailed Solution

We have the inequality|z|=|z+2z−2z|≤|z+2z|+2|z| Which implies|z|≤2+2|z|⇒|z|2≤2|z|+2|z|2−2|z|+1≤1+2⇒(|z|−1)2≤3⇒−3≤|z|−1≤3⇒1−3≤|z|≤1+3That is ,the maximum value of |z| is 1+3

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