See the attachment for the problems.
- the image of the closed rectangular region...
- principal branch of the square root...
(See attached file for full problem description).© BrainMass Inc. brainmass.com March 4, 2021, 6:28 pm ad1c9bdddf
Proof. WE prove the following two things.
(1) Verify that A->A', B->B', C->C' and D->D'
In z plane, A<-> z=0, B<->z=1-i, C<->z=1, D<->z=1+i
So, by mapping w(z)=z^2, we have
w(A)=0^2=0, w(B)=(1-i)^2=-2i, w(C)=1^2=1 and w(D)=(1+i)^2=2i
which correspond to A', B', C' and D' in the w-plane, respectively.
We are done.
(2) Triangle ABC is mapped to a parabola
To prove this case, we want to show
(a) the segment BD: x=1, y ...
This solution is comprised of a detailed explanation to solve the image of the closed rectangular region and the principal branch of the square root.