Sketch the following region in the complex plane: $\displaystyle { z \epsilon\mathbb{C} : |z -1| + |z + i| \leq 2}$

Attempt:

$\displaystyle |z - 1| + |z + i| \leq 2$

$\displaystyle \sqrt{(x - 1)^2 + y^2} + \sqrt{x^2 + (y + 1)^2} \leq 2$

$\displaystyle \sqrt{(x - 1)^2 + y^2} \leq 2 - \sqrt{x^2 + (y + 1)^2}$

$\displaystyle x^2 - 2x + 1 + y^2 \leq 4 - 4\sqrt{x^2 + y^2 + 2y + 1} + (x^2 + y^2 + 2y + 1)$

$\displaystyle -2x - 4 - 2y \leq -4\sqrt{x^2 + y^2 + 2y + 1}$

$\displaystyle (-2x - 4 - 2y)^2 \leq 16(x^2 + y^2 + 2y + 1)$

$\displaystyle 4x^2 + 16x + 16y + 8xy + 16 + 4y^2 \leq 16(x^2 + y^2 + 2y + 1)$

It looks like I have reached a dead end