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Question

If z is a complex number satisfying |z3+z3|2, then the maximum possible value of  |z+z1| is
  1. 2
  2. 32
  3. 22
  4. 1


Solution

The correct option is A 2
|z3+z3|2
Let, |z+z1|=a|(z+z1)3|=a3
|z3+z3+3(z+z1)|=a3
|z3+z3|+3aa3
a33a2a33a20
(a2)(a+1)20 
|z+z1|=a2
|z+z1|max=2

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