Results 1 to 3 of 3

Math Help - Trigonometry / Complex Numbers Question

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    2

    Trigonometry / Complex Numbers Question

    Given that z = cos A + j sin A , show that

    z + z + 2 + (1/z) + (1/(z)) = 2 cos A ( 2 cos A + 1 )

    can someone help me prove?? urgent
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ngwixn View Post
    Given that z = cos A + j sin A , show that

    z + z + 2 + (1/z) + (1/(z)) = 2 cos A ( 2 cos A + 1 )

    can someone help me prove?? urgent
    Are you familiar with deMoivre's theorem? Then:

    z^2 = \text{cis} (2A) = \cos (2A) + j \sin (2A).

    \frac{1}{z^2} = z^{-2} = \text{cis} (-2A) = \cos (-2A) + j \sin (-2A) = cos (2A) - j \sin (2A).

    \frac{1}{z} = z^{-1} = \text{cis} (-A) = \cos (-A) + j \sin (-A) = cos A - j \sin A.

    So the left hand side of the identity is equal to 2 \cos (2A) + 2 \cos A + 2.

    From here you should be able to substitute from the appropriate double angle formula and simplify to get 2 \cos A ( 2 \cos A + 1 ) .....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2008
    Posts
    2
    Thanks alot
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. complex numbers question
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: February 28th 2010, 08:10 AM
  2. complex numbers and trigonometry
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: January 14th 2010, 01:12 PM
  3. Complex numbers/trigonometry:
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 5th 2009, 10:25 AM
  4. complex numbers and trigonometry
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: November 29th 2009, 12:34 PM
  5. Complex numbers question
    Posted in the Pre-Calculus Forum
    Replies: 10
    Last Post: November 3rd 2008, 12:35 PM

Search Tags


/mathhelpforum @mathhelpforum