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

Correct Answer is : x<0,y>0x<0, y>0x<0,y>0

Correct Answer is : x<0,y>0x<0, y>0x<0,y>0

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AP EAPCET 04-Jul-2022 Shift 1 Paper

Section: Mathematics

Question : 8 of 160

Marks: +1, -0

\; \frac{x-1}{3+i} + \; \frac{y-1}{3-i} = i

i

then the true statement among the following is

Solution: 👈: Video Solution

\; \frac{x-1}{3+i} + \; \frac{y-1}{3-i} = i

\Rightarrow \; \frac{(x-1)(3-i)+(y-1)(3+i)}{(3+i)(3-i)} = i

\Rightarrow \; \frac{3x - i x - 3 + i + 3y + i y - 3 - i}{9 - i^2} = i

\Rightarrow 3x+3y - i x + i y - 6 = i[9-(-1)]

\Rightarrow 3x+3y - i x + i y - 6 = 10i

\Rightarrow 3(x+y) + i(-x+y) = 6+10i

On comparing both the sides, we get

3(x+y)=6

and

-x+y=10

\Rightarrow x+y=2

.....(i)

and

-x+y=10

.....(ii)

On solving Eqs. (i) and (ii); we get

2y=12 \Rightarrow y=6 \; \text{ and } \; x=-4

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