Mathematics: Find all the complex roots. write the answer in the indicated form. the complex cube roots of 27(cos 234° + i sin 234°) (polar form) a. 3(cos 78° + i sin 78°), 3(cos198° + i sin 198°), 3(cos 318° + i sin 318°) b. 3(cos 78° + i sin 78°), 3(cos 118° + i sin 118°), 3(cos 158° + i sin 158°) c. -3(cos 78° + i sin 78°), 3(cos 118° + i sin 118°), -3(cos 158° + i sin 158°) d. -3(cos 78° + i sin 78°), 3(cos 198° + i sin 198°), -3(cos 318° + i sin 318°)

Find all the complex roots. write the answer in

Ответ:

elishaheart21

15.03.2022

$\bf \textit{ roots of complex numbers, DeMoivre's theorem}
\\\\
\sqrt[n]{z}=\sqrt[n]{r}\left[ cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\ sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad 
\begin{array}{llll}
k\ roots\\
0,1,2,3,...
\end{array}\\\\
-------------------------------$

$\bf z=27[cos(234^o)+i~sin(234^o)]
\\\\\\
\sqrt[3]{z}\implies \sqrt[3]{27}\left[ cos\left( \cfrac{234^o+360^o(0)}{3} \right) +i\ sin\left( \cfrac{234^o+360^o(0)}{3} \right)\right]
\\\\\\
3\left[ cos\left( \cfrac{234^o}{3} \right) +i\ sin\left( \cfrac{234^o}{3} \right)\right]\implies \stackrel{k=0~~1st~root}{3[cos(78^o)+i~sin(78^o)]}\\\\
-------------------------------$

$\bf \sqrt[3]{z}\implies \sqrt[3]{27}\left[ cos\left( \cfrac{234^o+360^o(1)}{3} \right) +i\ sin\left( \cfrac{234^o+360^o(1)}{3} \right)\right]
\\\\\\
3\left[ cos\left( \cfrac{594^o}{3} \right) +i\ sin\left( \cfrac{594^o}{3} \right)\right]\implies \stackrel{k=1~~2nd~root}{3[cos(198^o)+i~sin(198^o)]}\\\\
-------------------------------$

$\bf \sqrt[3]{z}\implies \sqrt[3]{27}\left[ cos\left( \cfrac{234^o+360^o(2)}{3} \right) +i\ sin\left( \cfrac{234^o+360^o(2)}{3} \right)\right]
\\\\\\
3\left[ cos\left( \cfrac{954^o}{3} \right) +i\ sin\left( \cfrac{954^o}{3} \right)\right]\implies \stackrel{k=2~~3rd~root}{3[cos(318^o)+i~sin(318^o)]}$

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Ответ:

quynhnguyen7454

29.03.2020

Mathematics

Two things wrong here are
1. The questionnaire should be in the form of a table with tally marks and all that.
2. She should specify how much they spend per week, per month, per year or in how much time they spent that much money.
I hope this helped!!!

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