Find real value of `x ` and ` y` for which the complex numbers `-3+i x^2y ` and ` x^2+y+4i` are conjugate of each other.

Explanation

Given, `-3 + ix^(2)y = (barx^(2) + y+ 4i)`
or `" " -3 +ix^(2)y = x^(2) + y -4i`
or `" "-3 =x^(2) +y`
and `x^(2)y = -`
`therefore " "-3 = x^(2) -(4)/(x^(2))" "["Putting" = - 4//x^(2) "from (2) in (1)"]`
or `x^(4) +3x^(2) - 4=0`
or `(x^(2) + 4) (x^(2) -1) =0`
or `x^(2) -1=0`
or `x = pm 1`
From (2), `y = - 4`, when `x =pm1`. Hence, `x=1, y =-4 or x = - 1, y = - 4`