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AP EAMCET202319 May 2023Morning ShiftMathematicsComplex NumberActual

Arg ( 4+2 i 1-2 i + 3+4 i 2+3 i ) lies in the interval

Options

  1. A( 4 , 2 )
  2. B(- , - 2 )
  3. C( - 2 , 0 )
  4. D(0, 4 )

Correct answer

A. ( 4 , 2 )

Step-by-step solution

aligned & ( 4+2 i 1-2 i + 3+4 i 2+3 i ) & = (4+2 i)(2+3 i)+(3+4 i)(1-2 i) (1-2 i)(2+3 i) & = (2+16 i)+(11-2 i) (8-i) = (13+14 i) (8-i) & = 90+109 i 64+1 = 90 65 + 109 65 i & ( 4+2 i 1-2 i + 3+4 i 2+3 i )= ( 90 65 + 109 65 i ) & = ⁻¹ ( 109 90 )= ⁻¹(1.21) aligned Since 4 =1 and 2 = Therefore, 4 < ( 4+2 i 1-2 i + 3+4 i 2+3 i ) < 2

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