Представим число z=-7+7i в виде r(cosa+isina) r=14 cosa=-1/2 sina=1/2 Откуда a=3π/4 Тогда 5 значений корня:
![\sqrt[5]{z} =w_k, k=0,1,2,3,4](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bz%7D+%3Dw_k%2C+k%3D0%2C1%2C2%2C3%2C4 "\sqrt[5]{z} =w_k, k=0,1,2,3,4")
![w_k= \sqrt[5]{14} (cos( \frac{ \frac{3 \pi }{4} +2 \pi k}{5} )+isin( \frac{\frac{3 \pi }{4} +2 \pi k}{5} ))](https://tex.z-dn.net/?f=w_k%3D+%5Csqrt%5B5%5D%7B14%7D+%28cos%28+%5Cfrac%7B++%5Cfrac%7B3+%5Cpi+%7D%7B4%7D++%2B2+%5Cpi+k%7D%7B5%7D+%29%2Bisin%28+%5Cfrac%7B%5Cfrac%7B3+%5Cpi+%7D%7B4%7D+%2B2+%5Cpi+k%7D%7B5%7D+%29%29 "w_k= \sqrt[5]{14} (cos( \frac{ \frac{3 \pi }{4} +2 \pi k}{5} )+isin( \frac{\frac{3 \pi }{4} +2 \pi k}{5} ))")