Question

Find real values of x and y for which -3+ix^2y and x^2+y+4i are conjugates of each other?

Answer 1

`x,y = pm 1, -4`

Explanation:

If `-3+ix^2y` and `x^2+y+4i` are conjugates, then:

• `-3= x^2+y qquad square`

• `x^2y =color(red)(-) 4 qquad triangle`

Sub `triangle` into `square`:

`-3= - 4/y +y`

`y^2 + 3y - 4 = 0`

`(y + 4)(y - 1 ) = 0 implies y = -4, 1`

From `triangle`:

• `x = sqrt ( - 4/y)`

For a real x, choose `y = -4 implies x = pm 1`

`x,y = pm 1, -4`