equality in integral inequality for compelx functions











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I am trying to understand why:



$left|displaystyle{int}_{gamma}fleft(zright)dzright|=displaystyle{int}_{gamma}left|fleft(zright)right||dz|iffforall z$ on $gamma$ it is $text{arg}left(fleft(zright)right)=text{const.}$



where $int_gamma f(z)|dz|:=int_a^bf(gamma(t))|gamma'(t)|dt$



can someone direct me? Thank you.






integration complex-analysis complex-numbers complex-integration







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  • That identity is for some $gamma$ or for all $gamma$?
    – ajotatxe
    yesterday










  • @ajotatxe $gamma$ is a path, any path
    – user3708158
    yesterday

















up vote
2
down vote

favorite












I am trying to understand why:



$left|displaystyle{int}_{gamma}fleft(zright)dzright|=displaystyle{int}_{gamma}left|fleft(zright)right||dz|iffforall z$ on $gamma$ it is $text{arg}left(fleft(zright)right)=text{const.}$



where $int_gamma f(z)|dz|:=int_a^bf(gamma(t))|gamma'(t)|dt$



can someone direct me? Thank you.






integration complex-analysis complex-numbers complex-integration







share|cite|improve this question
























  • That identity is for some $gamma$ or for all $gamma$?
    – ajotatxe
    yesterday










  • @ajotatxe $gamma$ is a path, any path
    – user3708158
    yesterday















up vote
2
down vote

favorite









up vote
2
down vote

favorite











I am trying to understand why:



$left|displaystyle{int}_{gamma}fleft(zright)dzright|=displaystyle{int}_{gamma}left|fleft(zright)right||dz|iffforall z$ on $gamma$ it is $text{arg}left(fleft(zright)right)=text{const.}$



where $int_gamma f(z)|dz|:=int_a^bf(gamma(t))|gamma'(t)|dt$



can someone direct me? Thank you.






integration complex-analysis complex-numbers complex-integration







share|cite|improve this question















I am trying to understand why:



$left|displaystyle{int}_{gamma}fleft(zright)dzright|=displaystyle{int}_{gamma}left|fleft(zright)right||dz|iffforall z$ on $gamma$ it is $text{arg}left(fleft(zright)right)=text{const.}$



where $int_gamma f(z)|dz|:=int_a^bf(gamma(t))|gamma'(t)|dt$



can someone direct me? Thank you.






integration complex-analysis complex-numbers complex-integration




integration complex-analysis complex-numbers complex-integration






share|cite|improve this question















share|cite|improve this question













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edited 21 hours ago









JustDroppedIn

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asked yesterday









user3708158

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1066












  • That identity is for some $gamma$ or for all $gamma$?
    – ajotatxe
    yesterday










  • @ajotatxe $gamma$ is a path, any path
    – user3708158
    yesterday




















  • That identity is for some $gamma$ or for all $gamma$?
    – ajotatxe
    yesterday










  • @ajotatxe $gamma$ is a path, any path
    – user3708158
    yesterday


















That identity is for some $gamma$ or for all $gamma$?
– ajotatxe
yesterday




That identity is for some $gamma$ or for all $gamma$?
– ajotatxe
yesterday












@ajotatxe $gamma$ is a path, any path
– user3708158
yesterday






@ajotatxe $gamma$ is a path, any path
– user3708158
yesterday

















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