Results 1 to 4 of 4

Math Help - complex numbers

  1. #1
    blondie89
    Guest

    Question complex numbers

    Hello, would really appreciate if anyone could answer this questions for me ... i'm really stuck! If possible, could you show all working out because otherwise i will get lost!

    * Find all the fifth roots of - 1.

    * Find all the third roots of 2 + 2 i .

    *3. If w = (z - i)/(z+i) and z lies below the real axis, show that w lies outside the unit circle
    | w | = 1.
    How will w move as z travels along the real axis from - infinity to + infinity ?

    *4. Prove that the area A ( a, b, c ) of the triangle in the complex plane with corners at a, b, c
    must be C (Complex), ordered in anti-clockwise fashion, is given by the formula:
    A ( a, b, c ) = (i/4)( ab` - a`b + b c `- b`c + c a` - c`a )

    Thank you !
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    You can't get ANY of these?

    1 and 2 require ONLY DeMoivre. Convert the values to polar coordinates and you should see it.

    The third looks like an algebra problem. It could be a little messy, I guess.

    Let's see if you can get through those while I think about #4, or someone else chimes in.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    the first two questions were dealt with here. i like Soroban's method the most
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Note that (-1)^{1/5} = -1. If you let \zeta = \cos \frac{2\pi}{5}+i\sin \frac{2\pi }{5}. Then the roots are -1,-\zeta,-\zeta^2.-\zeta^3.-\zeta^4.
    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

/mathhelpforum @mathhelpforum