Solve the equation `|z|=z+1+2i`

Explanation

`|z|= z+1 + 2i`
`rArr sqrt(x^(2) + y^(2)) = x + iy + 1+ 2i =x+1+(2+y)i`
`rArr sqrt(x^(2) + y^(2)) = x + 1 and 0=2 +y or y = -2`
`rArr sqrt(x^(2) + 4)) = x+1`
`or x^(2) + 4 = x^(2) + 2x + 1`
`or 2x = 3`
`or x=(3)/(2)`
`rArr x + iy = (3)/(2)-2i`