Sketch inequalities in the complex plane

Sketch each of the following sets of complex numbers $z$ that satisfy the given inequalities:

Letting $z = x+ iy$ we have,
$\begin{align*} |2z+3| < 1 && \implies && |2x+3 + 2yi| &< 1 \\ && \implies && \sqrt{(2x+3)^2 + 4y^2} &< 1 \\ && \implies && (2x+3)^2 + 4y^2 < 1. \end{align*}$

This is a disk of radius $\frac{1}{2}$ centered at $\left(-\frac{3}{2}, 0 \right)$ . The sketch is as follows:
Letting $z = x+ iy$ we have,
$\begin{align*} |z+1| < |z-1| && \implies && \sqrt{(x+1)^2 +y^2} &< \sqrt{(x-1)^2 + y^2} \\ && \implies && x^2 + 2x + 1 + y^2 &< x^2 -2x + 1 + y^2 \\ && \implies && 4x &< 0 \\ && \implies && x &< 0. \end{align*}$

This is the half-plane with negative real part. The sketch is as follows:
Letting $z = x + iy$ we have,
$\begin{align*} |z-i| \leq |z+i| && \implies && \sqrt{x^2 + (y-1)^2} &\leq \sqrt{x^2 + (y+1)^2} \\ && \implies && x^2 + y^2 - 2y + 1 &\leq x^2 + y^2 + 2y + 1 \\ && \implies && y & \geq 0. \end{align*}$

This is the half-plane with positive imaginary part. The sketch is as follows:
Letting $z = x+ iy$ we have,
$\begin{align*} |z| \leq |2z+1| && \implies && \sqrt{x^2+y^2} &\leq \sqrt{(2x+1)^2 + (2y)^2} \\ && \implies && x^2 + y^2 &\leq 4x^2 + 4x + 1 + 4y^2 \\ && \implies && 0 &\leq 3x^2 + 4x + 1 + 3y^2 \\ && \implies && 0 &\leq x^2 + \frac{4}{3}x + \frac{4}{9} + y^2 - \frac{1}{9} \\ && \implies && \frac{1}{9} &\leq \left( x +\frac{2}{3} \right)^2 + y^2. \end{align*}$

This is the region outside the disk of radius $\frac{1}{3}$ centered at the point $\left( -\frac{2}{3}, 0 \right)$ . The sketch is as follows:

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