Mathematics, 23.07.2019 17:30 NEUROPHARMACOLOGICAL
Which expression is a cube root of -2i? 1) 3sqrt2(cos(210))+isin(210)) 2) 3sqrt2(cos(260))+isin(260)) 3) 3sqrt2(cos(90))+isin(90)) 4) 3sqrt2(cos(60))+isin(60))
Answers: 1
![Z=(-2 i)^{\frac{1}{3}}\\\\Z^3= -2 i\\\\Z^3=2[0- i]\\\\z^3=2[\cos(\frac{3\pi }{2})+i \sin(\frac{3\pi }{2})]\\\\z=2^{\frac{1}{3}}[\cos(\frac{3\pi }{2})+i \sin(\frac{3\pi }{2})]^{\frac{1}{3}}\\\\z=2^{\frac{1}{3}}[\cos(2k\pi +\frac{3\pi }{2})+i \sin(2k\pi +\frac{3\pi }{2})]^{\frac{1}{3}}\\\\z=2^{\frac{1}{3}}[\cos(\frac{2k\pi}{3} +\frac{\pi }{2})+i \sin(\frac{2k\pi}{3} +\frac{\pi }{2})]^{\frac{1}{3}}\\\\ \text{use Demoiver's theorem}}\\\\ (\cos A + \sin A)^n=\cos nA +i\sin nA\\\\ \text{for, k=0,}}](/tpl/images/0124/2225/de590.png)
![(-2 i)^{\frac{1}{3}},\text{which is equal to }}=2^{\frac{1}{3}}[\cos(\frac{\pi }{2})+i \sin\frac{\pi }{2})]](/tpl/images/0124/2225/3d77b.png)
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Which expression is a cube root of -2i? 1) 3sqrt2(cos(210))+isin(210)) 2) 3sqrt2(cos(260))+isin(260...
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