Question

If $-3+x^{2}yi$ and $x^2+y+4i$ are conjugate of each other, then find $|x|+|y|$.

Answer 1

since, $-3+x^{2}yi$ & $x^2+y+4i$ are conjugate of each other
Therefore, $-3+x^{2}yi=x^2+y-4i$
on comparing real parts & imaginary parts, we get
$-3=x^2+y$ ...(1)
$x^{2}y=-4$ ...(2)
from (1) & (2), we get
$x=1$ & $y=-4$
Therefore, $\left|x\right|+\left|y\right|=5$

Ans: 5