#algebra 

If $\LARGE z=r(\cos(\theta)+i\sin(\theta))$ (z is a [[Комплексные числа|complex number]]), then:
> $$\LARGE z^n=r^n(\cos(n\theta)+i\sin(n\theta))$$

(формула Муавра)
## Proof
![[Pasted image 20240917185919.png]]

## Application
Can be applied to find [[Комплексные числа#^213d80|nth roots of a complex number]]