– meyli $n$ sanı 2 ge teń yamasa onnan úlken natural san bolsın. $z$ sannan $n$-dárejeli koreni dep, $u^n=z$ teńligi orınlı bolatuǵın $u$ kompleks sanǵa aytıladı. $z$ kompleks sannan $n$-dárejeli koren tómendegi formula boyınsha tabılatuǵın dál $n$ mániske iye: $$\begin{array}{lll}\beta&=&\sqrt[n]{z}=\sqrt[n]{r(\cos\varphi+i\sin\varphi)}=\\ [1mm]&=&\sqrt[n]{r}\left(\cos\dfrac{\varphi+2\pi k}{n}+i\sin\dfrac{\varphi+2pi k}{n}\right),\end{array}$$ bunda $k$ sanı $n$ sandaǵı $0, 1, 2, \ldots, n-1$ mánislerdi qabıl etiwi múmkin, $r$ - kompleks sannıń moduli, al $\varphi$ - onıń argumenti. $n=2$ bolǵanda $z$ kompleks sannıń kvadrat koreni ushın $$\beta=\sqrt{r}\left(\cos\dfrac{\varphi+2\pi k}{2}+i\sin\dfrac{\varphi+2\pi k}{2} \right)$$ formulası orınlı, bunda $k=0, 1$ yamasa $k=0$ bolǵanda $\beta_0=\sqrt{r}\left(\cos\dfrac{\varphi}{2}+i\sin\dfrac{\varphi}{2}\right)$, $k=1$ bolǵanda $\beta_1=\sqrt{r}\left(\cos\left(\dfrac{\varphi}{2}+\pi\right)+i\sin\left(\dfrac{\varphi}{2}+\pi\right) \right)$.