DIVISIONS OF PURE IMAGINARY NUMBERS: three application exercises

The division of pure imaginary numbers is carried out as follows:
Division of pure imaginary numbers
(i_a) / (i_b) = a/b
where a and b are real numbers.
Examples
1. (i_2) / (i_3) = 2/3
2. (i_4) / (i_5) = 4/5
3. (i_1) / (i_2) = 1/2
Division Properties
1. It is not commutative: (i_a) / (i_b) ≠ (i_b) / (i_a)
2. It is not associative: ((i_a) / (i_b)) / (i_c) ≠ (i_a) / ((i_b) / (i_c))
Division of pure imaginary numbers with real numbers
(i_a)/b = (i_a)/b
Examples
1. (i_2) / 3 = i_2/3
2. (i_4) / 2 = i_2
Calculation software
1. MATLAB
2. Mathematica
3. Python (NumPy library)
4. Wolfram Alpha