Hi everybody

I need some help to solve this complex equation:

(√3 + i − e^{z}) (e^{z}-1) = 0

that has a modulus smaller than 3π.

I'm thinking about using zero product property:

e^{z}- 1 = 0

z = ln(1)

z = 0

but when it comes to the first parenthesis I don't know how to proceed.

Thank you.