#algebra 

## Definition
Let us have a [[Комплексные числа|complex]]-valued function $\LARGE f(z)$ in some domain so that $\LARGE \frac{df}{dz}\neq0$ anywhere in that domain

Let's think of that function as a mapping between complex plane $\LARGE z$ and complex plane $\LARGE f$
![[Pasted image 20251025003735.png]]

The mapping that doesn't change the angle between crossing curves, and transforms infitesimal circles into infinitesimal circles is called a **conformal mapping**

It's crucial that the modulus of the derivative is non-zero, and usually all [[Holomorphic function|holomorphic]] functions are conformal mappings
In reality they also have to be [[Отображение#^b7fa1c|injective]] 

>Application: change of variables in integrals

Example:
![[Pasted image 20251025010529.png]]