When you’re adding or subtracting complex numbers, it’s easy to make some mistakes. Here are some common issues I’ve noticed, along with tips to help you avoid them:

1. Forgetting About the Imaginary Unit

One big mistake is forgetting that $i$, the imaginary unit, means $\sqrt{-1}$.

When you add or subtract, it’s important to remember to include the $i$.

For example, if you’re adding $(2 + 3i)$ and $(4 + 5i)$, think of it like this:

• Combine the real parts: $2 + 4 = 6$
• Combine the imaginary parts: $3i + 5i = 8i$

So, the answer is $6 + 8i$.

2. Not Combining Like Terms

Make sure to combine the real parts and the imaginary parts separately.

Like terms help a lot!

For example, if you subtract $(7 + 2i)$ from $(3 + 5i)$, do it this way:

• Start with $3 - 7$ for the real parts.
• Then do $5i - 2i$ for the imaginary parts.

You get $-4 + 3i$. If you skip this step, you might get the wrong answer.

3. Overlooking Parentheses

When you see complex numbers in parentheses, don’t forget about them!

For example, when subtracting $(2 + 4i)$ from $(5 - 3i)$, you need to make sure to distribute the negative sign correctly.

Here’s how it should look:

• $5 - 3i - 2 - 4i$

If you ignore the parentheses, you could mess up your signs and get the wrong result.

4. Mixing Up Multiplication and Addition

Watch out! Don’t confuse multiplication with addition.

When you add complex numbers, you simply combine like terms.

But when you multiply them, you have to use the distributive property.

You also need to keep track of your $i$s, especially if $i^2$ comes into play.

5. Mismanaging Final Forms

Finally, remember to write your answer in standard form, which is $a + bi$.

If you end up with something like $2 + -1i$, you should rewrite it as $2 - i$.

This makes everything look neat and is easier for you and others to understand.

Keep these tips in mind, and you’ll find adding and subtracting complex numbers much easier!