Recent content by h0llow

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    Solving Roots of Unity with De Moivre's Theorem

    o you oops :P thanks so much!... the word unity kind of confused me =/
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    Solving Roots of Unity with De Moivre's Theorem

    0_o z3=1+0i = (1+0i)1/3...r=1 θ=0 z1 = (1(cos0+isin0))1/3 1(1+0) =1 z2 = (1(cos2∏+isin2∏))1/3 1(cos(2∏/3)+isin(2∏/3)) = -1/2 + √3/2 z3 = (1(cos(4∏)+isin(4∏))1/3 =1(cos(4∏/3)+isin(4∏/3)) =-1/2 - √3/2 1+(-1/2+√3/2)+(-1/2 - √3/2) = 0! Thank you so much! Maths is...
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    Solving Roots of Unity with De Moivre's Theorem

    okay, i understand the cube part. Can you just tell me how you would go about solving it?
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    Solving Roots of Unity with De Moivre's Theorem

    how do you know they are cube roots? Angle is the same for all values of n?(even integers) EDIT: no, this is the first time i have seen a question like this. The maths course in my country is currently changing(introduced in phases), so not everything is in books(99% is, but 1% like this...
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    Solving Roots of Unity with De Moivre's Theorem

    well ^3, but I am not sure why it is significant.
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    Solving Roots of Unity with De Moivre's Theorem

    (r(cosθ+isinθ))n=rneinθ hmm I am guessing for 1, n= 0 for ω, n=1 for ω2, n = 2
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    Solving Roots of Unity with De Moivre's Theorem

    (r(cosθ+isinθ))n
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    Solving Roots of Unity with De Moivre's Theorem

    r(cos(θ + 2n∏)+isin(θ+isin∏))?
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    Solving Roots of Unity with De Moivre's Theorem

    Homework Statement Use De Moivre's Theorem to solve for the roots of unity 1, ω, ω2 Hence show that the sum of these roots is zero Homework Equations r(cosθ + isinθ) r(cos(θ + 2n∏)+isin(θ+isin∏)) The Attempt at a Solution I know the first root,1, is 1(cos 0 + i sin 0) but have no clue about...
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    Undergrad Math puzzle that involve thought process

    thx for replies, i got the answer..quite easy when u think about it.
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    Split Prize Money for Head & Tails Game: 6 Wins vs 4 Wins Ratio

    is the answer by any chance 81.25% and 18.75% splits in prize?
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    Split Prize Money for Head & Tails Game: 6 Wins vs 4 Wins Ratio

    TT = 25% likely TTHHH,etc.. = 3.125% likely (since there are 5(0.5^5))...X 8 HTT = 12.5%(0.5^3) X 2 HHTT = 6.25% X 4 everything adds up to 100% 0_o..what now.. the t's look fine :o
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    Split Prize Money for Head & Tails Game: 6 Wins vs 4 Wins Ratio

    nvm.. i got it...can u tell me if i am right though? TT THHT HHHH HTT HTHT HTHHH HHTT THHHT THHHH HHHTT THTH HHTHH THT HHTHT HHHTH = 15 possibilities chance player A (T) wins = 10/15 = 66.67% chance player B (H) wins = 5/15 = 33.33% am i...
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    Split Prize Money for Head & Tails Game: 6 Wins vs 4 Wins Ratio

    nvm.. i got it...can u tell me if i am right though? TT THHT HHHH HTT HTHT HTHHH HHTT THHHT THHHH HHHTT THTH HHTHH THT HHTHT HHHTH = 15 possibilities chance player A (T) wins = 10/15 = 66.67% chance player B (H) wins = 5/15 = 33.33% am i right?
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    Split Prize Money for Head & Tails Game: 6 Wins vs 4 Wins Ratio

    so i should write out all the 120 possibilities? (5!)