# What are complex numbers?

As you may know, you can’t add or subtract two different variables to get one. For example, 4a + 3a = 7a but 4a + 3b is still equal to 4a + 3b. In the case of the sum or difference of an imaginary number and a real number, you get a complex number:

but

and, more in general, a complex number is written as follows:

where *a* and *b* are real numbers.

Let’s now introduce the complex plane:

As you can see, instead of “x” we have Re (real) and instead of “y” Im (imaginary). Also, the point *a*+*bi* has coordinates (*a*; *b*), and since *b* is on the Im axis is an imaginary number, *bi*. This is why *a*+*bi* is between the two axis: it’s got **a real part**, *a*, and **an imaginary part**, *b*.

**Re and Im functions**

What is the real part of 4-3i? And what’s the imaginary part? Simply put, the former is the number without the imaginary unit *i*, the latter is the number that has the *i* next to it. The function which gives as output the real part of a complex number is Re(), whereas for the imaginary part it is Im().

You can use ( ) instead of { }, but I prefer the latter. It also looks cooler, doesn’t it?

Examples:

Now give this a try and leave your answer in the comments!

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