Subtracting Imaginary Numbers

Subtracting two imaginary numbers involves simply subtracting their imaginary coefficients: $$ (0,a) - (0,b) = (0,a-b) $$ Expressed in algebraic form, where (0,b) = bi, the subtraction looks like this: $$ a i - b i = (a-b)i $$

Example

Let's consider two imaginary numbers:

$$ (0,5) = 5i $$ $$ (0,3) = 3i $$

The difference between these two numbers is (0,2):

$$ (0,5) - (0,3) = (0,5-3) = (0,2) $$

When written in algebraic form, the subtraction yields the same result:

$$ 5i - 3i = (5-3)i = 2i $$

Note: Both forms represent the same imaginary number: 2i = (0,2). Since the imaginary unit is a constant (i = (0,1)), the imaginary number 2i can be expressed in algebraic form by multiplying the real number 2 by the imaginary unit (0,1): $$ 2i = 2 \cdot (0,1) = (2 \cdot 0, 2 \cdot 1) = (0,2) $$

And so forth.