Complex Numbers on the ACT: Addition and Subtraction

Complex Numbers

Complex numbers are kind of like binomials. They have two parts: a real number and an imaginary number. Some examples of complex numbers would be (3 + 4i) , (-2, -i), or (7 – 3i). Make sense? We’ve got the real and the imaginary working together in peace and harmony.

Let’s talk about what you can do with them.


Addition and Subtraction

There are two ways to think about adding and subtracting complex numbers: the simple way and the smarty-pants-math way. We’ll take a quick look at both.

The Simple Way

Combine like terms. Seriously, that’s it.

Okay, fine, we can do an example.


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We’ll add our real numbers first, then the imaginary ones.


So our answer is 1 + 3i.

Simple, yeah? Let’s try subtraction. Watch out for the negative signs!


So our answer is -3 – 2i.

The Smarty-Pants-Math Way

Who likes to memorize formulas? I hear lots of crickets chirping out there, but let’s look at it anyway.

You can think of a complex number as a + bi. In this case, the a and b can be substituted by any real number.

So, if you want to add two of them together, you get this:


Make sense? Combine a and c like we did in The Simple Way, then combine b and d, tacking the i on at the end.

Let’s look at subtraction.


Easy enough, right? These are all operations you should be really familiar with, so hopefully this was a piece of cake!


By the way, Magoosh can help you study for both the SAT and ACT exams. Click here to learn more!

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