Reverse Triangle Inequality/Real and Complex Fields/Corollary 1/Proof 3

Proof
Let $z_1$ and $z_2$ be represented by the points $A$ and $B$ respectively in the complex plane.

From Geometrical Interpretation of Complex Subtraction, we can construct the parallelogram $OACB$ where:
 * $OA$ and $OB$ represent $z_1$ and $z_2$ respectively
 * $BA$ represents $z_1 - z_2$.


 * Complex-Reverse-Triangle-Inequality-Corollary.png

But $OA$, $OB$ and $BA$ form the sides of a triangle.

The result then follows directly from Sum of Two Sides of Triangle Greater than Third Side.