Results 1 to 8 of 8

Math Help - Complex numbers are complexing

  1. #1
    Member M670's Avatar
    Joined
    Sep 2012
    From
    Montreal
    Posts
    142

    Complex numbers are complexing

    There are only two complex arithmetic problems on this set, since you have seen complex numbers before. This one is a little involved, however. You may want to make judicious use of a calculator or a symbol manipulation language like Maple. Of course there is a reason for the fancy real and imaginary parts, and your final expression for will tell you that reason.



    Enter the following powers of in the standard form of a complex number:

    ___________ ____________ .
    ___________ ____________ .
    ___________ ____________ .
    ___________ ____________ .
    _______________________ .
    I don't have maple but I figured out z=.309016 and then all my other answer where wrong? but if my z=0.309016 can I not just square and cube it and some on?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,786
    Thanks
    1570

    Re: Complex numbers are complexing

    Quote Originally Posted by M670 View Post
    There are only two complex arithmetic problems on this set, since you have seen complex numbers before. This one is a little involved, however. You may want to make judicious use of a calculator or a symbol manipulation language like Maple. Of course there is a reason for the fancy real and imaginary parts, and your final expression for will tell you that reason.



    Enter the following powers of in the standard form of a complex number:

    ___________ ____________ .
    ___________ ____________ .
    ___________ ____________ .
    ___________ ____________ .
    _______________________ .
    I don't have maple but I figured out z=.309016 and then all my other answer where wrong? but if my z=0.309016 can I not just square and cube it and some on?
    How could z possibly be 0.309016? You know that z is complex (and in fact, already have z), what makes you think it is real?

    I expect you are supposed to put z into a polar form so you can evaluate \displaystyle \begin{align*} z^5 \end{align*} using DeMoivre's Theorem. From there it might be easier to evaluate the other powers of z.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member M670's Avatar
    Joined
    Sep 2012
    From
    Montreal
    Posts
    142

    Re: Complex numbers are complexing

    Sorry the real part of Z was 0.309016 but the Imaginary part I didn't get it right
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,910
    Thanks
    1759
    Awards
    1

    Re: Complex numbers are complexing

    Quote Originally Posted by M670 View Post
    There are only two complex arithmetic problems on this set, since you have seen complex numbers before. will tell you that reason.
    [CENTER]


    Enter the following powers of in the standard form of a complex number:
    This is really interesting question.

    You can show that |z|=1

    Using a computer algebra system, I can see that z^5=1.
    But I do not know how to do it 'by hand'.

    Some way we must show that \text{Arg}(z)=\left(\frac{2\pi}{5}\right). But I have no clue how.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member M670's Avatar
    Joined
    Sep 2012
    From
    Montreal
    Posts
    142

    Re: Complex numbers are complexing

    Why would they ask such a complicated question ....lol
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member M670's Avatar
    Joined
    Sep 2012
    From
    Montreal
    Posts
    142

    Re: Complex numbers are complexing

    can I not solve it by z=a+bi then (a+bi)(a+bi) to get z^2
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member M670's Avatar
    Joined
    Sep 2012
    From
    Montreal
    Posts
    142

    Re: Complex numbers are complexing

    Does this need to be solved by using De Moivre Theorem ?
    Quote Originally Posted by Plato View Post
    This is really interesting question.

    You can show that |z|=1

    Using a computer algebra system, I can see that z^5=1.
    But I do not know how to do it 'by hand'.

    Some way we must show that \text{Arg}(z)=\left(\frac{2\pi}{5}\right). But I have no clue how.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,910
    Thanks
    1759
    Awards
    1

    Re: Complex numbers are complexing

    Quote Originally Posted by M670 View Post
    Does this need to be solved by using De Moivre Theorem ?

    Well, the answer to that is clearly yes.
    But I have absolutely no idea how to get \frac{2\pi}{5} out of the given.

    It is not hard to show that |z|=1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. raising complex numbers to complex exponents?
    Posted in the Advanced Math Topics Forum
    Replies: 10
    Last Post: March 25th 2011, 11:02 PM
  2. Replies: 1
    Last Post: September 27th 2010, 04:14 PM
  3. Replies: 2
    Last Post: February 7th 2009, 07:12 PM
  4. Replies: 1
    Last Post: May 24th 2007, 04:49 AM
  5. Complex Numbers- Imaginary numbers
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 24th 2007, 01:34 AM

Search Tags


/mathhelpforum @mathhelpforum