Mathematics, 15.07.2020 04:01 assassin42
Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fourth roots of -9i.
A. Type an exact answer in the first answer box.
B. Type any angles in degrees between o and 360 needed.)
C. Type all degree measures rounded
Answers: 1
![z^{\frac{1}{n} } = [r(cos\theta + isin\theta)]^{\frac{1}{n} } \\z^{\frac{1}{n} } = \sqrt[n]{r} (cos(\frac{\theta+2nk}{n} ) + isin(\frac{\theta+2nk}{n}))](/tpl/images/0706/9161/b21a4.png)
is the argument
![z_k^{\frac{1}{4} } = \sqrt[4]{9} (cos(\frac{90+2(4)k}{4} ) + isin(\frac{90+2(4)k}{4}))\\z_k^{\frac{1}{4} } = \sqrt[4]{9} (cos(\frac{90+8k}{4} ) + isin(\frac{90+8k}{4}))\\](/tpl/images/0706/9161/e095b.png)
![z_0 = \sqrt[4]{9} (cos(\frac{90}{4} ) + isin(\frac{90}{4}))\\z_0 = \sqrt[4]{9} (cos(23) + isin(23))\\\\when\ k =1\\z_1 = \sqrt[4]{9} (cos(\frac{90+8}{4} ) + isin(\frac{90+8}{4}))\\z_1 = \sqrt[4]{9} (cos(25 ) + isin(25))\\\\when\ k =2\\z_2 = \sqrt[4]{9} (cos(\frac{90+16}{4} ) + isin(\frac{90+16}{4}))\\z_2 = \sqrt[4]{9} (cos(27 ) + isin(27))\\\\when\ k =3\\z_3 = \sqrt[4]{9} (cos(\frac{90+24}{4} ) + isin(\frac{90+24}{4}))\\z_3 = \sqrt[4]{9} (cos(29 ) + isin(29))\\](/tpl/images/0706/9161/b2f7d.png)
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Find all the complex roots. Leave your answers in polar form with the argument in degrees. The compl...
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