Triangle Inequality for Complex Numbers (|z₁ + z₂| ≤ |z₁| + |z₂|)
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|z₁ + z₂| ≤ |z₁| + |z₂|
What each symbol means
| Symbol | What it stands for |
|---|---|
| Equality | Holds with equality iff z₁, z₂ have same argument (same direction from origin) |
| z_1, z_2 | Any two complex numbers |
When to use this
True for all z₁, z₂ ∈ ℂ. Geometrically: one side of triangle ≤ sum of other two sides in Argand plane.