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Question

If z4z=2, then the greatest value of |z| is


A

1+2

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B

2+2

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C

3+1

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D

5+1

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Solution

The correct option is D

5+1


We have
|z|=z4z+4zz4z+4|z|=2+4|z||z|22|z|+4(|z|1)25|z|15|z|5+1
Also, for z=5+1,z4z=2
Therefore, the greatest value of |z| is 5+1 which is attained when z=5+1


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