Triangle Inequality/Complex Numbers/Examples/3 Arguments/Proof 1
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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 $n = 3$.
$\blacksquare$