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Homework Help: Complex Analysis - Finding the image through a mapping

  1. Mar 11, 2012 #1
    1. The problem statement, all variables and given/known data
    The point 1 + i is rotated anticlockwise through [itex]\frac{∏}{6}[/itex] about the origin. Find its image.

    3. The attempt at a solution

    The point 1 + i creates an angle of arctan(1/1) = ∏/4

    The rotation is by a further angle β = ∏/6.

    So the new point w in the w-plane from the mapping would be:

    w = r.exp(iθ + β)

    w = √2.exp(∏/4 + ∏/6)
    w = √2(cos 5∏/12 + i.sin 5∏/12)

    Is this correct?
  2. jcsd
  3. Mar 11, 2012 #2
    looks correct yes
  4. Mar 11, 2012 #3
    Thank you.
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