Find branches F, G of log(z), both analytic at 1 and i, such that: Im F(1) > Im F(i) Im G(1) > Im G(i)

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Find branches F, G of log(z), both analytic at 1 and i, such that: Im F(1) > Im F(i) Im G(1) > Im G(i)

I think I know how to do it, I'm just little confused about what "branches" mean. When it says branches, does it mean in the form log theta (z), 0