Hi,

Use De’Moivre’s theorem to solve the following equations:

a. X^(3) - 1 = 10

b. (x + 1)^(5) + x^(2) = 0

Thanks in advance,

Lalit Chugh

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- June 19th 2006, 12:11 PMlalitchughDe'Moivre's theorem
Hi,

Use De’Moivre’s theorem to solve the following equations:

a. X^(3) - 1 = 10

b. (x + 1)^(5) + x^(2) = 0

Thanks in advance,

Lalit Chugh - June 19th 2006, 02:34 PMThePerfectHackerQuote:

Originally Posted by**lalitchugh**

Express in polar form thus,

Thus,

for

Thus,

- June 19th 2006, 06:40 PMmalaygoelQuote:

Originally Posted by**ThePerfectHacker**

- June 19th 2006, 06:59 PMThePerfectHackerQuote:

Originally Posted by**malaygoel**

We can then show that if,

Then,

Furthermore, all elements are distinct.

Thus, by the pigeonhole principle we have exactly elements in this set. But since a polynomial can have a most solution we see that all of the solution of, are found in this set.

I like to think this is as elegant as it gets.

Yes you can take other values for , but I like to follow this reasoning. Because, I am certain that all the solutions are found by starting at k=0 and going to k=n-1. - June 19th 2006, 10:33 PMlalitchughProblem reg De'Moivre's theorem
Hi,

Many thanks for the solution.

May i request you to provide solution for 2nd question on De'Moivre's thoerem as well.

I will be thankful to you. It will help me in undertstanding the steps.

Best Regards,

Lalit Chugh - June 21st 2006, 06:22 AMThePerfectHacker
latichugh do not beg!

-=USER WARNED=-

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Your question was not answered perhaps because it has nothing with de Moiver's theorem.