Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    6
    ReputationRep:
    The question is {w = e^{ix}} is a cube root of 1, state the three values of x in the range -pi < x < pi and find the possible values of {(1 - w)^{6}}

    For the possible values of x, I have got 2pi/3, -2pi/3 and 0. I also know that 1 + w + w^2 = 0 although I don't know how to move from there.

    Thanks in advance.
    Offline

    11
    ReputationRep:
    (Original post by Quido)
    The question is {w = e^{ix}} is a cube root of 1, state the three values of x in the range -pi < x < pi and find the value of {(1 - w)^{6}}
    Should that be 1-w^6?
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by Quido)
    The question is {w = e^{ix}} is a cube root of 1, state the three values of x in the range -pi < x < pi and find the value of {(1 - w)^{6}}

    For the possible values of x, I have got 2pi/3, -2pi/3 and 0. I also know that 1 + w + w^2 = 0 although I don't know how to move from there.

    Thanks in advance.
    "The" value of {(1 - w)^{6}}?? It gives 2 different ones depending on which x you pick, unless you meant this part to be something different.
    • Thread Starter
    Offline

    6
    ReputationRep:
    (Original post by atsruser)
    Should that be 1-w^6?
    Nope, the 6 is outside the bracket unless it is a misprint
    • Thread Starter
    Offline

    6
    ReputationRep:
    (Original post by RDKGames)
    "The" value of {(1 - w)^{6}}?? It gives 2 different ones depending on which x you pick, unless you meant this part to be something different.
    Sorry, I was meant to write the possible values of (1 - w)^6
    Changed now.
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by Quido)
    Sorry, I was meant to write the possible values of (1 - w)^6
    Changed now.
    Ah that's better.

    Okay so 1-w is given by 1-e^{ix} for x \in \{ 0, \frac{2}{3}\pi , -\frac{2}{3}\pi \}

    Then you just consider each case separately.

    For 1-e^{\pm \frac{2}{3}\pi i} it would be useful to express this in cartesian form first before expressing it in the form re^{i\theta} then raising this to the 6th power.
    Online

    17
    ReputationRep:
    Well, one value for (1-w)^6 should be easy...

    For the others, draw 1-w on an argand diagram. Some basic geometry should let you express 1-w in Re^{i\ttheta} form without too much work.
    Online

    17
    ReputationRep:
    PS: if you want to do it without an Argand diagram, I think you'll find life a bit easier if you observe that

    1-e^{ix} = e^{ix/2} (e^{-ix/2} - e^{ix/2}) and the term in brackets can be rewritten as -2i sin(x/2).
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by DFranklin)

    1-e^{ix} = e^{ix/2} (e^{-ix/2} - e^{ix/2}) and the term in brackets can be rewritten as -2i sin(ix/2).
    Typo? :ninja:
    Online

    17
    ReputationRep:
    (Original post by RDKGames)
    Typo? :ninja:
    Well, brain-fart...
    • Thread Starter
    Offline

    6
    ReputationRep:
    Alright, I've got it now. Thanks everyone!
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Will you be richer or poorer than your parents?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.