Let f(z) = sqrt(z) be the branch of the square root function with sqrt(z) = (r^1/2) (e^iΘ/2),
0≤Θ<2[itex]\pi[/itex], r > 0
(a) for what values of z is sqrt(z^2) = z?
(b) Which part of the complex plane stretches, and which part shrinks under this transformation?
The Attempt at a Solution
Ok so for this branch i believe the function will map all points within 0≤Θ<2[itex]\pi[/itex] to the upper half plane (ie Im(f) > 0).
I do not really understand what part a is asking and for part b it seems everything is shrunk.