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

Correct answer: (B) x 0. (x-1)/(3+i)+(y-1)/(3-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

Q48 / 160 · AP EAMCET 2022 (04 Jul Shift 1) · Mathematics

If $\frac{x - 1}{3 + i} + \frac{y - 1}{3 - i} = i$ then the true statement among the following is

A
$x < 0, y < 0$
Correct answer
B
$x < 0, y > 0$
C
$x > 0, y < 0$
D
$x > 0, y < 0$

Solution

$\frac{x - 1}{3 + i} + \frac{y - 1}{3 - i} = i$
$\Rightarrow (x - 1) (3 - i) + (y - 1) (3 + i) = i (3 + i) (3 - i)$
$\Rightarrow 3 x - 3 - i x + i + 3 y - 3 + i y - i = 10 i$
$\Rightarrow 3 x + 3 y - 6 - i x + i y = 10 i$
$\Rightarrow y - x = 10 & x + y - 2 = 0$
i.e. $x = - 4, y = 6$

Hence, the correct answer is option: 'B'.

If x-13+i+y-13-i=i then the true statement among the following is

Solution

Relevant Questions

If $\frac{x - 1}{3 + i} + \frac{y - 1}{3 - i} = i$ then the true statement among the following is