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JEE Main2017MathematicsComplex NumberActual

Let z ∈ C , the set of complex numbers. Then the equation, 2 z + 3 i - z - i = 0 represents:

Options

  1. AA circle with radius 8 3
  2. BAn ellipse with length of minor axis 16 9
  3. CAn ellipse with length of major axis 16 3
  4. DA circle with diameter 10 3

Correct answer

A. A circle with radius 8 3

Step-by-step solution

Let z = x + i y so that 2 x + i y + 3 = x + i y - 1 ⇒ 2 x 2 + y + 3 2  =  x 2 + y - 1 2 ⇒ 4 x 2 + 4 y + 3 2 = x 2 + y - 1 2 ⇒ 3 x 2 + 3 y 2 +26 y + 35 = 0 ⇒ x 2 + y 2 + 26 3 y + 35 3 = 0 ⇒ r =   0 + 169 9 - 35 3 ⇒ r = 64 9 = 8 3

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