# I made a mistake with $$e$$ in $$\mathbb{C}$$, but I ammended it

Calculus Level 4

True or false? (In $$\mathbb{C}$$) $\displaystyle \lim_{z \to 0} (e^{z})^{\frac{1}{z}} = e$

Note.- We are using the exponentiaton complex, and not the multivalued function or multifunction "$$\text{ exp(z)}$$" ,i.e, if $$h : \mathbb{C} - \{0\} \longrightarrow \mathbb{C}$$ is the function $$h(z) = (e^{z})^{\frac{1}{z}}$$ then $\displaystyle \lim_{z \to 0} h(z) = e, \text{ is true or false ?}$ Bonus.- what about $$\displaystyle \lim_{z \to 0} (e^{\frac{1}{z}})^{z} = e$$?

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