ADDITION AND SUBTRACTION OF PURE IMAGINARY NUMBERS: APPLICATION EXERCISE

The addition of imaginary numbers is done in a similar way to the addition of complex numbers. The formula is:
Sum of imaginary numbers
(z1 + z2) = (a1 + a2) + (b1 + b2)i
where:
1. z1 = a1 + b1i
2. z2 = a2 + b2i
Examples
1. (2 + 3i) + (1 + 2i) = (2 + 1) + (3 + 2)i = 3 + 5i
2. (1 - 2i) + (3 + 4i) = (1 + 3) + (-2 + 4)i = 4 + 2i
Properties of sum
1. *Comutative*: z1 + z2 = z2 + z1
2. *Associative*: (z1 + z2) + z3 = z1 + (z2 + z3)
3. *Neutral element*: z + 0 = z
Subtraction of imaginary numbers
The subtraction is done in a similar way:
Subtraction of imaginary numbers
(z1 - z2) = (a1 - a2) + (b1 - b2)i
Examples
1. (2 + 3i) - (1 + 2i) = (2 - 1) + (3 - 2)i = 1 + i
2. (1 - 2i) - (3 + 4i) = (1 - 3) + (-2 - 4)i = -2 - 6i
Calculation software
1. MATLAB
2. Mathematica
3. Python (NumPy library)
4. Wolfram Alpha