Triangle Inequality/Complex Numbers/Examples/3 Arguments/Proof 1

Example of Use of Triangle Inequality for Complex Numbers

For all $z_1, z_2, z_3 \in \C$:

$\cmod {z_1 + z_2 + z_3} \le \cmod {z_1} + \cmod {z_2} + \cmod {z_3}$

Proof

This is an instance of the General Triangle Inequality for Complex Numbers:

$\cmod {z_1 + z_2 + \dotsb + z_n} \le \cmod {z_1} + \cmod {z_2} + \dotsb + \cmod {z_n}$

setting $n = 3$.

$\blacksquare$