Question Number 35478 by 7991 last updated on 19/May/18
$$\sqrt[{\mathrm{5}}]{\mathrm{3}\sqrt{\mathrm{2}}\left(\mathrm{2}−{i}\right)}=…?? \\ $$
Commented by MJS last updated on 19/May/18
$$\mathrm{these}\:\mathrm{are}\:\mathrm{all}\:\mathrm{the}\:\mathrm{same} \\ $$$${z}={a}+{b}\mathrm{i}={r}\mathrm{e}^{\varphi\mathrm{i}} ={r}\mathrm{cos}\left(\varphi\right)+{r}\mathrm{sin}\left(\varphi\right)\mathrm{i} \\ $$$${z}^{\frac{{p}}{{q}}} ={r}^{\frac{{p}}{{q}}} \mathrm{e}^{\frac{{q}\varphi}{{p}}\mathrm{i}} ={r}^{\frac{{p}}{{q}}} \mathrm{cos}\left(\frac{{q}\varphi}{{p}}\right)+{r}^{\frac{{p}}{{q}}} \mathrm{sin}\left(\frac{{q}\varphi}{{p}}\right)\mathrm{i} \\ $$