If x - 1 3 + i + y - 1 3 - i = i then the true statement among the following is

If x-13+i+y-13-i=i then the true statement among the following is
  1. x<0,y<0
  2. x<0,y>0
  3. x>0, y<0
  4. x>0,y<0

Solution

x-13+i+y-13-i=i

⇒x-13-i+y-13+i=i3+i3-i

⇒3x-3-ix+i+3y-3+iy-i=10i

⇒3x+3y-6-ix+iy=10i

⇒y-x=10 & x+y-2=0

i.e. x=-4, y=6

Asked in: AP EAMCET 2022 (04 Jul Shift 1)

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