Solve that equation `z^2+|z|=0` , where `z` is a complex number.

Explanation

`z^(2) + |z|=0`
`rArr x^(2) -y^(2) + i(2xy) + sqrt(x^(2) + y^(2)) = 0`
`rArr x^(2) - y^(2) + sqrt(x^(2) + y^(2)) = 0" "(1)`
and ` 2xy = 0" "(2)`
From (2), let x= 0 . From (1),
`-y^(2) + sqrt(y^(2)) = 0`
`rArr -|y|^(2) + |y| = 0`
`rArr |y| = 0 or 1`
`rArr y = 0 or y = pm 1`
From (2), if y = 0 , then from (1),
`x^(2)+ sqrt(x^(2)) = 0`
`rArr |x|^(2) +|x|=0`
`rArr x = 0`
Hence, complex numbers are `0 + i0, 0+i,0-i`