When we add or subtract complex numbers, we need to pay attention to the real and imaginary parts separately.

Let's look at two complex numbers: $a + bi$ and $c + di$.

1. Adding Complex Numbers:

   • First, we add the real parts: $a + c$.
   • Next, we add the imaginary parts: $b + d$.
   • The final answer looks like this: $(a + c) + (b + d)i$.

   For example, if we take $(2 + 3i)$ and $(4 + 5i)$:

   • We add the real parts: $2 + 4 = 6$.
   • We add the imaginary parts: $3 + 5 = 8$.
   • So, $(2 + 3i) + (4 + 5i) = 6 + 8i$.

2. Subtracting Complex Numbers:

   • First, we subtract the real parts: $a - c$.
   • Then, we subtract the imaginary parts: $b - d$.
   • The answer will be: $(a - c) + (b - d)i$.

   For example, if we take $(7 + 2i)$ and $(3 + 1i)$:

   • We subtract the real parts: $7 - 3 = 4$.
   • We subtract the imaginary parts: $2 - 1 = 1$.
   • So, $(7 + 2i) - (3 + 1i) = 4 + 1i$.

In both cases, we handle the real and imaginary parts separately, which makes everything a lot easier!