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NTA Abhyas JEE Main2020MathematicsComplex NumberPractice

For the complex number z satisfying the condition z + 2 z = 2 , the maximum value of z is

Options

  1. A3 - 1
  2. B3 + 1
  3. C2 + 3
  4. D3

Correct answer

B. 3 + 1

Step-by-step solution

| z | − | 2 | z | | ≤ | z + 2 z | ≤ | z | + | 2 | z | | Now, for maximum or minimum value of | z | , LHS inequality will hold true as it corresponds to the two complex numbers being on opposite sides of origin. Hence, | z | − 2 | z | ≤ 2 (without loss of generality let LHS > 0) ⇒ | z | 2 − 2 | z | − 2 ≤ 0 ⇒ | z | ≤ 2 + 4 + 8 2 ⇒ | z | ≤ 1 + 3

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