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Let P h , k be a point on an argand plane equidistant from the roots of the equation z + 1 4 = 16 z 4 , then the value of h is equal to

Options

  1. A0
  2. B2 3
  3. C1 3
  4. D1 2

Correct answer

C. 1 3

Step-by-step solution

z + 1 z 4 = 16 ⇒ z + 1 z = 2 or - 2 or 2 i or - 2 i Hence, the roots are 1 ,   - 1 3 ,   - 1 5 - 2 5 i and - 1 5 + 2 5 i i.e. the roots are equidistant from the centre of the circle as shown in the figure. 1 3 , 0 is the centre of the circle. Hence, h = 1 3

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