![\bf \sqrt[{{ n}}]{z}=\sqrt[{{ n}}]{r}\left[ cos\left( \frac{\theta+2\pi k}{{{ n}}} \right) +i\ sin\left( \frac{\theta+2\pi k}{{{ n}}} \right)\right]\quad k\ roots\\\\ -------------------------------\\\\](/tpl/images/0430/9812/1fddc.png)
![\bf \sqrt[3]{64}[cos(330^o)+i\ sin(330^o)] \\\\\\ \sqrt[3]{64}\left[cos\left( \frac{330+360(0)}{3} \right) + i\ sin\left( \frac{330+360(0)}{3} \right) \right] \\\\\\ 4[cos(110^o)+i\ sin(110^o)]\implies 4(-0.34202014)+4(0.9396926) \\\\\\ \approx -1.37 + 3.76i\impliedby \textit{first root, k = 0}\\\\ -------------------------------\\\\](/tpl/images/0430/9812/54a70.png)
![\bf \sqrt[3]{64}[cos(330^o)+i\ sin(330^o)] \\\\\\ \sqrt[3]{64}\left[cos\left( \frac{330+360(1)}{3} \right) + i\ sin\left( \frac{330+360(1)}{3} \right) \right] \\\\\\ 4[cos(230^o)+i\ sin(230^o)]\implies 4(-0.6427876)+4(-0.7660444) \\\\\\ \approx -2.57 -3.06i\impliedby \textit{second root, k = 1}\\\\ -------------------------------\\\\](/tpl/images/0430/9812/f9de3.png)
![\bf \sqrt[3]{64}[cos(330^o)+i\ sin(330^o)] \\\\\\ \sqrt[3]{64}\left[cos\left( \frac{330+360(2)}{3} \right) + i\ sin\left( \frac{330+360(2)}{3} \right) \right] \\\\\\ 4[cos(350^o)+i\ sin(350^o)]\implies 4(0.98480775)+4(-0.1736481) \\\\\\ \approx 3.94 -0.695i\impliedby \textit{third root, k = 2}](/tpl/images/0430/9812/5a20c.png)
cube root 64(cos330+isin330)
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Mathematics, 23.12.2019 22:31 carter283
cube root 64(cos330+isin330)
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