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Math Help - Pls help me with this complex number problem

  1. #1
    varun
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    Question Pls help me with this complex number problem

    If 1,w,w^2 are the cube roots of unity , then find the value of
    (1+w)(1+w^2)(1+w^3)(1+w^4)(1+w^5)
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  2. #2
    Junior Member
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    Quote Originally Posted by topsquark View Post
    Hint: w^2 = w. (First of all, can you prove this?)

    -Dan
    You mean w^3=1?
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by math sucks View Post
    You mean w^3=1?
    Ahem!

    Um, yeah, what I wrote was kinda silly, wasn't it?

    What I was trying to remember was this:
    w = a + ib \implies w^2 = a - ib

    But thinking about it a bit further I see there is a simpler way:
    w^4 = w
    and
    w^5 = w^2

    So your expression becomes
    2(1 + w)^2(1 + w^2)^2

    Now note that
    (1 + w)^2 = w
    and
    (1 + w^2)^2 = w^2

    -Dan
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