Once mathematicians were faced with equations that could not be solved using ordinary numbers:

To solve the problem and still find the root of the equation, they came up with the number i, which they called the imaginary unit.

And they also announced that this number is equal to the square root of minus one:

The square of this number is, respectively, equal to minus one:

Thanks to the imaginary unit, the solution of such equations became possible:

This is how complex numbers appeared, for which, in addition to the normal, understandable part, there was also an incomprehensible part where i is:

It turns out that the complex number z consists of two parts: a is called the real part, and b is the imaginary part of the complex number.

Complex plane

We have already worked with the plane. The points on it were marked with a pair of numbers x and y.

But what is a complex plane and where to get it?

To get a complex plane, you just need to do a small "rebranding" of the plane we are used to: replace the x axis with the re (real part) axis, and the y - with im (imaginary part).

On the resulting plane, you can now mark any complex number, because it also consists of two components (re, im), like the coordinates (x, y) that are already familiar to us: