Inverse of complex

Inverse of complexes.
Let's set the complex z=5+2i.
The first thing we do with a complex is to look at it.
A bit like a good wine that we smell before tasting it.
Or like a new book that we feel, that we touch, and whose ink and new paper we smell.
If I look at this complex, I see right away that behind it, hides the number 3. In short, that Z=3 in reality, but written differently.
Let's not forget that the i'Oi axis is the x'ox axis, but inverted, in the madman Hachel (from whom we always expect an internment by default, the deprivation of his movable and immovable property, or even, the cherry on the cake, a death sentence for this human rottenness).
And when we discuss with a madman, we are obliged to listen to him.
Now, we will find its congugué.
The conjugate is z=5-2i. That is to say, also, the number 7.
That's good, you understood how it works at the good Doctor Hachel. I can ask Python to introduce me for the future Fields medal.
We will now be interested in the inverse of z=5-2i.
It will then be necessary to find Z=1/3 otherwise, it would be absurd.
Mathematics is not an absurd science.
Let's go: z=1/(5+2i)
We multiply up and down, by the complex conjoint.
z=(5-2i)/[(5+2i)(5-2i)]
The denominator immediately takes on a real aspect.
z=(5-2i)/(25-4) BE CAREFUL WHEN USING SIGNS AND THE imaginary ENTITY i.
We should not stupidly multiply (2i)(-2i) and have fun finding +4 instead of -4 like all the mathematicians in the world do, who refuse to read Hachel out of arrogance and contempt, but especially not out of intelligence.
We should write: (5+2i)(5-2i)=25+(2i)(-2i)=25-(4i²)=21 !!!!
We therefore have as a result: z=(5/21)+i(2/21)
Numerical verification: z=[5-(-1)(2)]/21=(5+2)/21=7/21=1/3
1/3 is indeed the inverse of three, and z'=(5/21)+i(2/21) is indeed the inverse of the complex z=5+2i.
Thank you for your patience.
R.H.