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AP EAMCET201923 Apr 2019Morning ShiftMathematicsComplex NumberActual

The points in the argand plane represented by the complex conjugates of (1+2 i, 2-3 i, 3-4 i )

Options

  1. Aare collinear
  2. Bform an equilateral triangle
  3. Cform an obtuse angled triangle
  4. Dform an acute angled triangle

Correct answer

C. form an obtuse angled triangle

Step-by-step solution

The complex conjugate of given points are in argand plane (A(1-2 i), B(2+3 i), C(3+4 i) ) So ( aligned a & =B C= 1+1 = 2 b & =C A= 4+36 = 40 c & =A B= 1+25 = 26 B & = a^2+c^2-b^2 2 a c = 2+26-40 2 2 26 & =- 12 4 13 =- 3 13 < 0 aligned ) So, point (A, B ) and (C ) represents the vertices of an obtuse angled triangle. Hence, option (c) is correct.

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