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NTA Abhyas JEE Main2020MathematicsComplex NumberPractice

The minimum value of 8 Z - 8 + 2 Z - 4 exists, when Z is equal to (where, Z is a complex number)

Options

  1. A2
  2. B1.5
  3. C0
  4. D1

Correct answer

D. 1

Step-by-step solution

Given expression is 8 Z - 1 + 2 Z - 2 = 6 Z - 1 + 2 Z - 1 + Z - 2 Now, minimum Z - 1 + Z - 2 is equal to 1 , when Z lies on the line segment joining Z = 1 and Z = 2 . And, minimum Z - 1 is equal to 0 , when Z = 1 ⇒ Minimum 6 Z - 1 + 2 Z - 1 + Z - 2 is equal to 0 + 2 1 = 2 at Z = 1

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