Circular Complex Interval Arithmetic KC

3.2 Circular Complex Interval Arithmetic $KC$

Circular complex arithmetic $KC$ consists of a complex number $C$ , acting as a center point and a real number $R$ acting as a radius of a circle in a two dimensional Cartesian space. As such any number that is within radius of the pivot is contained in the interval. The mathematical definition a complex circular interval $X ∈KC$ is as follows:

X ={a∈ C:(ℜ(a)- ℜ(xp))2+(ℑ(a)-ℑ(xp))2-k2r≤ 0}

Where $xr∈{r∈ R:r≥ 0}≡xr∈ R+$ as the radius of the circle and $xp∈ C$ as the center point in a two dimensional Cartesian coordinate system.

3.2.1 Singleton Interval
3.2.2 Empty Interval
3.2.3 Whole Interval
3.2.4 Normalized Interval

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