MULTIPLICATION OF PURE IMAGINARY NUMBERS: APPLICATION EXERCISES TWO DIFFERENT METHODS

Multiplication of pure imaginary numbers is carried out as follows:
Multiplication 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 = -6
2. (i_4) * (i_5) = -4*5 = -20
3. (i_1) * (i_2) = -1*2 = -2
Properties of multiplication
1. *Comutative*: (i_a) * (i_b) = (i_b) * (i_a)
2. *Associative*: ((i_a) * (i_b)) * (i_c) = (i_a) * ((i_b) * (i_c))
3. *Neutral element*: (i_a) * 1 = i_a
Multiplication of pure imaginary numbers with real numbers
(i_a) * b = i_a*b
Examples
1. (i_2) * 3 = i_2_3 = i_6
2. (i_4) * 2 = i_4_2 = i_8
Calculation software
1. MATLAB
2. Mathematica
3. Python (NumPy library)
4. Wolfram Alpha