complex integration paths

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I was doing this question and stuck at just simple point enter image description here

what is $[.]$ this symbol ? for homologous and homotopic part i will try to see what these terms are on internet.. butcan you help me what is i) part

But I would be obliged if you do all parts or give hints for all parts... but so far i am concerned very much with first part only.. is it greatest integer function or anything else ?