Find real values of `xa n dy`for which the complex numbers `-3+i x^2ya n dx^2+y+4i`are conjugate of each other.

Find real values of `xa n dy`for which the complex numbers `-3+i x^2ya

1.	Find real values of `xa n dy`for which the complex numbers `-3+i x^2ya n dx^2+y+4i`are conjugate of each other.
Answer» Correct Answer - `(x =1, y = -4) or (x = -1, y = -4)` `(-3+iyx^(2))=(bar(x^(2)+y+4i))` `rArr" "(-3+iyx^(2))=(x^(2)+y-4i)` `rArr" "(x^(2)+y+3)-(4+yx^(2))i = 0` `rArr" "x^(2)+y+3=0 and 4 + yx^(2) = 0` `rArr" "x^(2)+y = -3" "...(i)" "and yx^(2) = -4" "...(ii)`. Putting `x^(2) = (-3-y)` from (i) in (ii), we get `y(-3-y) = -4 rArr y^(2)+3y - 4 = 0 rArr (y+4)(y-1)=0 rArr y = -4 or y = 1`. Now, `y = 1 rArr x^(2) = -4 rArr x` is imaginary. So, y `in` 1. When y = -4, we get `x^(2) = (-3+4)=1 rArr x = +- 1`. `therefore" "(x =1, y = -4) or (x = -1, y = -4)`.