Question

find real values of x and y for which the complex numbers
$- 3 + {ix}^{2} y$


and
${x}^{2} + y + 4i$
are conjugate of each other. ​

Answer 1

Answer:

when y= 1, x= ±2i

when y=-4, x= ±1

Step-by-step explanation:

two complex numbers a +i b and c+i d are conjugates if

a = c

b = -d

comparing we have

${x}^{2} + y = - 3 \\ {x}^{2} = - 3 - y$

Also

${x}^{2} y = - 4 \\ ( - 3 - y)y = - 4 \\ {y}^{2} + 3y - 4 = 0 \\ {y}^{2} + 4y - y - 4 = 0 \\ y(y + 4) - 1(y + 4) = 0 \\ (y - 1)(y + 4) = 0 \\ y = 1 \: \: \: and \: y = - 4$

when y= 1, x= ±2i

when y=-4, x= ±1