Mixing
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
edited 21 hours ago
JustDroppedIn
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asked yesterday
user3708158
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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
edited 21 hours ago
JustDroppedIn
1,759419
asked yesterday
user3708158
1066
That identity is for some $gamma$ or for all $gamma$?
– ajotatxe
yesterday
@ajotatxe $gamma$ is a path, any path
– user3708158
yesterday
add a comment |
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
edited 21 hours ago
JustDroppedIn
1,759419
asked yesterday
user3708158
1066
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
edited 21 hours ago
JustDroppedIn
1,759419
asked yesterday
user3708158
1066
edited 21 hours ago
JustDroppedIn
1,759419
asked yesterday
user3708158
1066
edited 21 hours ago
JustDroppedIn
1,759419
edited 21 hours ago
JustDroppedIn
1,759419
edited 21 hours ago
JustDroppedIn
1,759419
1,759419
asked yesterday
user3708158
1066
asked yesterday
user3708158
1066
asked yesterday
user3708158
1066
1066
That identity is for some $gamma$ or for all $gamma$?
– ajotatxe
yesterday
@ajotatxe $gamma$ is a path, any path
– user3708158
yesterday
add a comment |
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
add a comment |
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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