Complex Analysis - Finding the image through a mapping

  • #1

Homework Statement


The point 1 + i is rotated anticlockwise through [itex]\frac{∏}{6}[/itex] about the origin. Find its image.


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?
 

Answers and Replies

  • #2
133
4
looks correct yes
 
  • #3
Thank you.
 

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