Let Z1, Z2,..., Zn be complex numbers such that Re zk> 0 and Re(zi... Zk) > 0 for 1 ≤ k ≤n. Show that log(zi... Zn) = log z₁ + ... + log zn, where log z is the principal branch of the logarithm. If the restrictions on the zk are removed, does the formula remain valid?

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