Adding Imaginary Numbers

To add two imaginary numbers, you simply add their imaginary parts together. $$ (0,a) + (0,b) = (0,a+b) $$ When expressed in algebraic form, where (0,b)=bi, the addition looks like this: $$ a i + b i = (a+b)i $$

Example

Consider the following two imaginary numbers:

$$ (0,2)=2i $$ $$ (0,3)=3i $$

Their sum is (0,5).

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

Expressing the imaginary numbers in algebraic form gives the same result:

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

Note: The imaginary number 5i is another way of representing (0,5). Since the imaginary unit i is defined as a constant, i=(0,1), we can write: $$ 5i = 5 \cdot (0,1) = (5 \cdot 0, 5 \cdot 1) = (0,5) $$

And so on.