Interval Analysis

9Complex intervals

The set ℂ of complex numbers together with an arithmetic on ℂ can be introduced in many ways. For engineers one usually defines ℂ as the set

and an arithmetic as for algebraic terms in ℝ. A more rigorous definition starts with pairs (a, b) ∈ ℝ² and an arithmetic which adds and subtracts entrywise but multiplies by

and divides by

if (c, d) ≠ (0, 0), cf. for instance Hille [148]. It is obvious that the resulting structures (ℂ, +, ...