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AP EAMCET202017 Sep 2020Evening ShiftMathematicsComplex NumberActual

If (x+i y= (3+2 i)(4-7 i)(12+13 i) (13-12 i)(2-3 i)(11+3 i) ), then (x^2+y^2= )

Options

  1. A1
  2. B2
  3. C( 1 2 )
  4. D3

Correct answer

C. ( 1 2 )

Step-by-step solution

Given, ( aligned z & =x+i y= (3+2 i)(4-7 i)(12+13 i) (13-12 i)(2-3 i)(11+3 i) |z| & = |3+2 i| |4-7 i| |12+13 i| |13-12 i| |2-3 i| |11+3 i| & = ( 3^2+2^2 ) ( 4^2+7^2 ) ( (12^2+13^2 . ) ( 13^2+12^2 ) ( 2^2+3^2 ) ( 11^2+3^2 ) aligned ) ( aligned = & 4^2+7^2 11^2+3^2 = 65 130 = 1 2 x^2+y^2 & = 1 2 or x^2+y^2= 1 2 aligned )

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