Triangle Inequality Applications

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Triangle Inequality Applications

## Formula

$$|z_1+z_2|\le|z_1|+|z_2|$$

$$|z_1-z_2|\le|z_1|+|z_2|$$

$$|z_1+z_2+z_3|\le|z_1|+|z_2|+|z_3|$$

More generally:

$$\left|\sum_{k=1}^{n}z_k\right|\le\sum_{k=1}^{n}|z_k|$$

## Usage

- Used to find upper bounds of complex expressions.

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