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Question

If |z|<31, then |z2+2zcosα| will be
  1. equal to 3+1
  2. less than 2
  3. more than 3+1
  4. equal to 2


Solution

The correct option is B less than 2
|z2+2zcosα||z|2+2|z||cosα|
|z2+2zcosα||z|2+2|z|
( max value of |cosα| is 1)
|z2+2zcosα|<(31)2+2(31)
|z2+2zcosα|<2

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