Answer
The graph is the half-plane (including the boundary) $y\ge -\dfrac{1}{2}.$
Work Step by Step
$\begin{align*}
\vert z+i\vert &\ge \vert z\vert \\
\vert (x+iy)+i\vert &\ge \vert x+iy\vert \\
\vert x +i(y+1)\vert &\ge \vert x +iy\vert \\
\sqrt{x^2 + (y+1)^2} &\ge \sqrt{x^2 + y^2} \\
x^2 + (y+1)^2 &\ge x^2 + y^2 \\
x^2+ y^2 + 2y + 1 &\ge x^2 + y^2 \\
2y+1 &\ge 0 \\
y &\ge -\frac{1}{2}
\end{align*}$
The graph is the half-plane (including the boundary) $y\ge -\dfrac{1}{2}.$
