# Complex Analysis - Finding the image through a mapping

1. Mar 11, 2012

### NewtonianAlch

1. The problem statement, all variables and given/known data
The point 1 + i is rotated anticlockwise through $\frac{∏}{6}$ 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. Mar 11, 2012

### conquest

looks correct yes

3. Mar 11, 2012

Thank you.