Understanding how to make adding and subtracting complex numbers easier can help you feel more confident in math. Let’s go through it step-by-step using some simple methods.

Step 1: Know the Parts

Complex numbers usually look like this: (a + bi). Here, (a) is the real part, and (b) is the imaginary part.

For example, let’s look at two complex numbers:

• (z_1 = 3 + 4i)
• (z_2 = 1 + 2i)

To add or subtract them, you need to work with the real parts and the imaginary parts.

Step 2: Adding Complex Numbers

To add two complex numbers, just add the real parts together and the imaginary parts together. Here’s how it works:

[ z_1 + z_2 = (3 + 4i) + (1 + 2i) ]

Breaking it down:

• Add the real parts: (3 + 1 = 4)
• Add the imaginary parts: (4i + 2i = 6i)

So, the answer is:

[ z_1 + z_2 = 4 + 6i ]

Step 3: Subtracting Complex Numbers

Subtracting is similar. Let’s use the same numbers:

[ z_1 - z_2 = (3 + 4i) - (1 + 2i) ]

Breaking it down:

• Subtract the real parts: (3 - 1 = 2)
• Subtract the imaginary parts: (4i - 2i = 2i)

So, the answer is:

[ z_1 - z_2 = 2 + 2i ]

Conclusion

By using these simple techniques, adding and subtracting complex numbers is much easier. Just remember to work with the real parts and imaginary parts separately. Happy calculating!