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AP EAMCET202021 Sep 2020Evening ShiftMathematicsComplex NumberActual

If (x+i y= 3 2+ ( )+i ( ) ), then (x^2+y^2= )

Options

  1. A(4 x-3 )
  2. B(4 x+3 )
  3. C0
  4. D1

Correct answer

A. (4 x-3 )

Step-by-step solution

It is given that, ( aligned x+i y & = 3 2+ +i = 3(2+ -i ) (2+ )^2+ ^2 x+i y & = 3(2+ ) 5+4 -i 3 5+4 x^2+y^2 & =(x+i y)(x-i y)= 9 (2+ )^2+ ^2 & = 9 5+4 4 x-3 & = 12(2+ ) 5+4 -3 & = 24+12 -15-12 5+4 = 9 5+4 x^2+y^2 & =4 x-3 aligned ) Hence, option (a) is correct.

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