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The function f(z) = e^(z+i*pi) has infinitely many points in the fiber of each point in its range.

(A) Find four points that map to 1

(B) The natural inverse of f(z), say g(z) maps each point in its domain to infinitely points, as with log(z). For example, g(1) is infinitely many points, including the four you provided in the first part of the problem.

i. Choose a branch of g(z)

ii. Sketch the domain of this branch

iii. Sketch the range of this branch

IV, Indicate which point in the set g(1) is the image of 1 under your branch.

i have tried using following formula:

f(z)= az +b/cz+d

f1(z)= z+d/c

f2(z)= 1/z

f3(z)= (-(ad-bc)/c^2)*z

f4(z)= z+a/c

but getting nothing. can anyone help me with this?