Complex Analysis - Finding the image through a mapping

[NewtonianAlch]

Homework Statement

The point 1 + i is rotated anticlockwise through $\frac{∏}{6}$ 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?

 

[conquest]

looks correct yes

 

[NewtonianAlch]

Thank you.