Rectangular Complex Interval Arithmetic RC

3.3 Rectangular Complex Interval Arithmetic $RC$

Rectangular complex arithmetic $RC$ consists of two intervals $IR$ representing the real $ℜ$ and imaginary $ℑ$ component of a complex number $C$ . Geometrically a rectangular complex interval is a box in Cartesian two-dimensional space. Given a rectangular complex interval $k ∈RC$ where the extraction operators $ℜi(k),ℑi(k)∈ IR$ are used to extract the real and imaginary components a rectangular complex consists of a set of all complex numbers $v∈ C$ that uphold:

----- ----- RC= {(ℜi(k)≤ℜ(v)≤ ℜi(k)∧ (ℑi(k)≤ℑ(v)≤ ℑi(k)}

3.3.1 Singleton Interval
3.3.2 Empty Interval
3.3.3 Whole Interval

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