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Question

Find the maximum value of |z| when z3z=2, where z being a complex number.

A
1+3
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B
3
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C
1+2
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D
1
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Solution

The correct option is C 3
We have,
|z|=z3z+3z
|z|z3z+3z [Using triangle inequality]
|z|2+3z [z3z=2]
|z|2+3z
|z|2+3|z|
|z|22|z|30
(|z|3)(|z|+1)0
1|z|3
Thus, the maximum value of |z| is 3.

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