find-solution-in-C-x-4-x-3-x-2-x-1-0-

Question Number 94479 by i jagooll last updated on 19/May/20

find solution in C

x^{4} + x^{3} + x^{2} + x + 1 = 0

Answered by john santu last updated on 19/May/20

\Rightarrow (x - 1) (x^{4} + x^{3} + x^{2} + x + 1) = 0

\Rightarrow x^{5} - 1 = 0

x^{5} = 1 \Rightarrow {(x^{5})}^{\frac{1}{5}} = {(e^{2 π i})}^{\frac{1}{5}}

\Rightarrow x = e^{(\frac{2 π + 2 π n}{5}) . i}

x_{1} = \cos (\frac{2 π}{5}) + i \sin (\frac{2 π}{5})

x_{2} = \cos (\frac{4 π}{5}) + i \sin (\frac{4 π}{5})

x_{3} = \cos (\frac{6 π}{5}) + i \sin (\frac{6 π}{5})

x_{4} = \cos (\frac{8 π}{5}) + i \sin (\frac{8 π}{5})

Commented by i jagooll last updated on 19/May/20

thank you sir