Picard's theorem states that in any arbitrarily small neighborhood of a singularity isolated essential z0 an analytic function f takes all finite complex values, with one exception, an infinite number of times. Since z = 0 for is an essential isolated singularity of f(z)= e^(1/z); find an infinite number of z in any neighborhood of z = 0 for which f(z) = i. Which is the only exception?. That is, what is the only value that does not take f(z)= e^(1/z)?

Picard's theorem states that in any arbitrarily small neighborhood of a singularity isolated essential z₀ an analytic function f takes all finite complex values, with one exception, an infinite number of times. Since z = 0 for is an essential isolated singularity of f(z)= e^(1/z); find an infinite number of z in any neighborhood of z = 0 for which f(z) = i. Which is the only exception?. That is, what is the only value that does not take f(z)= e^(1/z)?