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Graphical representation of complex numbers

  1. Feb 28, 2013 #1
    Hi there,

    eI have two numbers:

    z1 = 2 + i
    z2 = exp(iδ) * z1

    i are complex numbers and δ is a real number. I need to answer a question - what does the graphical representation of z2 have in relation to the graphical representation of z1.

    Thanks for any help!
     
  2. jcsd
  3. Feb 28, 2013 #2

    dx

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    Multiplying by exp(ia) is a rotation by the angle a.

    This looks like a homework question. We have a special forum for that here, so in future post such questions there, and also try to tell us a little about how you've attempted to solve it, so that the help you receive is more meaningful.
     
    Last edited: Feb 28, 2013
  4. Feb 28, 2013 #3
    Thanks a lot.

    I'm sorry for posting in wrong section. I'm totally new on this forum. And yes, it is a homework question. Of course, I tried to solve it myself, but the only thing I know is, that:

    e^(iδ) = cos δ + i sin δ

    And I would also like to know, what's the reason - why is it a rotation.
     
  5. Feb 28, 2013 #4

    dx

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    If you rotate a vector (x, y) by an angle θ, the components x' and y' of the rotated vector are

    x' = xcosθ - ysinθ
    y' = xsinθ + ycosθ

    Now a complex number z = x + iy is like a vector with components x and y. Multiply x + iy with exp(iθ) = cosθ + isinθ, and you will get x' + iy' with x' and y' as above.
     
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