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The question is: establish the inequality

|[itex]\int[/itex]e^{izz}dz| [itex]\leq[/itex] [itex]\pi[/itex](1-e^{-R2})/4R

on C {z(t) = Re^{it}, t [itex]\in[/itex] [0,[itex]\pi[/itex]/4, R>0

When i saw the modulus of an integral i thought ML inequality.

I think the length will be R[itex]\pi[/itex]/4 but im struggling with finding the maximum of e^{izz}. I tried changing to e^{i(r2(cos(2t)+isin(2t)}. but i dont feel any closer to the result.

Am i on the right track, and can anyone help me with finding the max of the function.

thanks

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# ML inequality question

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