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Question:

If |z - 4/z| = 2, then the maximum value of |z| is

2

2+√2

√3+1

√5+1

Solution:

|z - 4/z| = 2
Now, |z| = |z - 4/z + 4/z| ≤ |z - 4/z| + 4/|z| ≤ 2 + 4/|z|
⇒ |z|² - 2|z| - 4 ≤ 0
Solving quadratic inequality
1 - √5 ≤ |z| ≤ 1 + √5
⇒ 0 < |z| ≤ 1 + √5 (|z| can't be negative)