Results 1 to 6 of 6

Math Help - complex plane

  1. #1
    Junior Member
    Joined
    Dec 2007
    From
    University of California, Berkeley
    Posts
    48

    complex plane

    .

    .
    Last edited by yellow4321; March 6th 2008 at 05:10 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by yellow4321 View Post
    from previous question im told |a|=1
    if F is some map F:complex-->complex defined by F(z)=az how can i show the map F is a rotation. i know it will be a rotation because the angles will be added but i get confused about cos(theta)+isin(theta) where abouts on the argand diagram would this lie if cos(theta)+isin(theta)=1
    then suppose a=i what would be the rotation then?
    If |a|=1 then a=e^{i\theta} and so if z = |z|e^{i\arg (z)} then az = |z|e^{i\theta}e^{i\arg(z)} = |z|e^{i(\theta + \arg (z))} which is the same complex number by rotated \theta .

    This is Mine 85th Post!!!
    Last edited by ThePerfectHacker; January 26th 2008 at 02:33 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ThePerfectHacker View Post
    If |a|=1 then a=e^{i\theta} and so if z = |z|e^{i\arg (z)} then az = |z|e^{i\theta}e^{i\arg(z)} = |z|e^{i(\theta + \arg (z))} which is the same complex number by rotated \theta .
    It goes without saying (well, it nearly did ) that there's NO rotation if a = 1.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by mr fantastic View Post
    It goes without saying (well, it nearly did ) that there's NO rotation if a = 1.
    It is, it is called a "trivial rotation".
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Dec 2007
    From
    University of California, Berkeley
    Posts
    48
    thank you what if a=i ?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by yellow4321 View Post
    thank you what if a=i ?
    Let us see what happens. Pick a number, say 1+0i and graph it on the complex plane. If you multiply this by i we get 0+i. Pick a point as -1+0i multiply it by i and it becomes -i. Try it for \pm i. Can you guess what type of rotation this is?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: September 13th 2011, 07:16 AM
  2. Replies: 10
    Last Post: September 11th 2011, 12:06 AM
  3. Replies: 12
    Last Post: June 2nd 2010, 02:30 PM
  4. Euclidean plane vs the complex plane
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 16th 2010, 12:55 PM
  5. Replies: 2
    Last Post: December 3rd 2008, 06:26 PM

Search Tags


/mathhelpforum @mathhelpforum