Official solution
Given z = x + iy
|z| -- Re(z) \[ \le \] 1
\[ \Rightarrow \] \[\sqrt {{x^2} + {y^2}} \] - x \[ \le \] 1
\[ \Rightarrow \] \[\sqrt {{x^2} + {y^2}} \] \[ \le \] 1 + x
\[ \Rightarrow \] x2 + y2 \[ \le \] 1 + 2x + x2
\[ \Rightarrow \] y2 \[ \le \] 2x + 1
\[ \Rightarrow \] y2 \[ \le \] 2\[\left( {x + {1 \over 2}} \right)\]