1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex Vectors

  1. Jul 11, 2009 #1
    1. The problem statement, all variables and given/known data
    A complex vector is written as,
    [tex]\hat{v}(t) = cos(\omega t)\hat{x} + sin(\omega t)\hat{y} = \hat{x} + j\hat{y}[/tex],

    where [tex]\omega[/tex] is the angular velocity, and the vector rotates counterclockwise in the x-y plane.

    If a unit vector is rotated in the x-y plane but is phase shifted by 45degrees, then:

    [tex]\hat{v}(t) = (\frac{1}{\sqrt{2}} + j\frac{1}{\sqrt{2}})\hat{x} + \frac{1}{\sqrt{2}} - j\frac{1}{\sqrt{2}})\hat{x} \Rightarrow (cos(\omega t + 45^{\circ})\hat{x} + (cos(\omega t - 45^{\circ})\hat{y}[/tex]

    Can someone explain to me why there are terms [tex]\frac{1}{\sqrt{2}}[/tex] in the equation above. I always thought a 45 degree triangle had sides of [tex]\sqrt{2}, \sqrt{2}, 2[/tex], but not sure how the coefficient [tex]\frac{1}{\sqrt{2}}[/tex] is obtained.


  2. jcsd
  3. Jul 11, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi JL! :smile:

    (you've got your x's and y'x mixed up … and you can get LaTeX to write big brackets "to fit" by typing \left( and \right) :wink:)

    Because cos45º = sin45º = 1/√2 (a 45 degree triangle also has sides of 1, 1/√2, 1/√2) :smile:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Complex Vectors
  1. Complex Vectors rotation (Replies: 11)

  2. Complex power (Replies: 1)