Editing Complex number (section)

===Convergence===
[[File:ComplexPowers.svg|right|thumb|Illustration of the behavior of the sequence <math>z^n</math> for three different values of ''z'' (all having the same argument): for <math>|z|<1</math> the sequence converges to 0 (inner spiral), while it diverges for <math>|z|>1</math> (outer spiral).]]
The notions of [[convergent series]] and [[continuous function]]s in (real) analysis have natural analogs in complex analysis. A sequence <!--(''a''<sub>''n''</sub>)<sub>''n'' ≥ 0</sub>--> of complex numbers is said to [[convergent sequence|converge]] if and only if its real and imaginary parts do. This is equivalent to the [[(ε, δ)-definition of limit]]s, where the absolute value of real numbers is replaced by the one of complex numbers. From a more abstract point of view, <math>\mathbb{C}</math>, endowed with the [[metric (mathematics)|metric]]
<math display=block>\operatorname{d}(z_1, z_2) = |z_1 - z_2|</math>
is a complete [[metric space]], which notably includes the [[triangle inequality]]
<math display=block>|z_1 + z_2| \le |z_1| + |z_2|</math>
for any two complex numbers {{math|''z''<sub>1</sub>}} and {{math|''z''<sub>2</sub>}}.