Simplify product of complex numbers
up vote
1
down vote
favorite
I am trying to take product of a complex number with its conjugate. When I take
A*Conjugate[A] // FullSimplify
The output is as desired
Abs[A]^2
But when I try
FullSimplify@(A*Conjugate[A]*B*Conjugate[B])
The output is
A B Conjugate[A] Conjugate[B]
Why mathematica is not showing the output as
Abs[A]^2 Abs[B]^2
I am using Mathematica 11.2.0.
simplifying-expressions complex
asked Nov 10 at 11:45
Archimedes
156
add a comment |
up vote
1
down vote
favorite
I am trying to take product of a complex number with its conjugate. When I take
A*Conjugate[A] // FullSimplify
The output is as desired
Abs[A]^2
But when I try
FullSimplify@(A*Conjugate[A]*B*Conjugate[B])
The output is
A B Conjugate[A] Conjugate[B]
Why mathematica is not showing the output as
Abs[A]^2 Abs[B]^2
I am using Mathematica 11.2.0.
simplifying-expressions complex
asked Nov 10 at 11:45
Archimedes
156
ComplexExpanddoes the work:A*Conjugate[A]*B*Conjugate[B] // ComplexExpand.
– rmw
Nov 10 at 13:41
@rmw - You have letComplexExpandassume thatAandBare real-valued. The OP is working with complex variables.
– Bob Hanlon
Nov 10 at 15:29
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am trying to take product of a complex number with its conjugate. When I take
A*Conjugate[A] // FullSimplify
The output is as desired
Abs[A]^2
But when I try
FullSimplify@(A*Conjugate[A]*B*Conjugate[B])
The output is
A B Conjugate[A] Conjugate[B]
Why mathematica is not showing the output as
Abs[A]^2 Abs[B]^2
I am using Mathematica 11.2.0.
simplifying-expressions complex
asked Nov 10 at 11:45
Archimedes
156
I am trying to take product of a complex number with its conjugate. When I take
A*Conjugate[A] // FullSimplify
The output is as desired
Abs[A]^2
But when I try
FullSimplify@(A*Conjugate[A]*B*Conjugate[B])
The output is
A B Conjugate[A] Conjugate[B]
Why mathematica is not showing the output as
Abs[A]^2 Abs[B]^2
I am using Mathematica 11.2.0.
simplifying-expressions complex
simplifying-expressions complex
asked Nov 10 at 11:45
Archimedes
156
asked Nov 10 at 11:45
Archimedes
156
asked Nov 10 at 11:45
Archimedes
156
asked Nov 10 at 11:45
Archimedes
156
asked Nov 10 at 11:45
Archimedes
156
156
ComplexExpanddoes the work:A*Conjugate[A]*B*Conjugate[B] // ComplexExpand.
– rmw
Nov 10 at 13:41
@rmw - You have letComplexExpandassume thatAandBare real-valued. The OP is working with complex variables.
– Bob Hanlon
Nov 10 at 15:29
add a comment |
ComplexExpanddoes the work:A*Conjugate[A]*B*Conjugate[B] // ComplexExpand.
– rmw
Nov 10 at 13:41
@rmw - You have letComplexExpandassume thatAandBare real-valued. The OP is working with complex variables.
– Bob Hanlon
Nov 10 at 15:29
ComplexExpand does the work: A*Conjugate[A]*B*Conjugate[B] // ComplexExpand.– rmw
Nov 10 at 13:41
ComplexExpand does the work: A*Conjugate[A]*B*Conjugate[B] // ComplexExpand.– rmw
Nov 10 at 13:41
@rmw - You have let
ComplexExpand assume that A and B are real-valued. The OP is working with complex variables.– Bob Hanlon
Nov 10 at 15:29
@rmw - You have let
ComplexExpand assume that A and B are real-valued. The OP is working with complex variables.– Bob Hanlon
Nov 10 at 15:29
add a comment |
2 Answers
2
active
oldest
votes
up vote
1
down vote
accepted
You can use ComplexExpand
simplify =
Simplify[ComplexExpand[#, Variables[Level[#, -1]],
TargetFunctions -> Abs, Arg]] &;
A*Conjugate[A] // simplify
(* Abs[A]^2 *)
simplify[A*Conjugate[A]*B*Conjugate[B]]
(* Abs[A]^2 Abs[B]^2 *)
answered Nov 10 at 13:33
Bob Hanlon
58.2k23594
Thank you. This will save a lot of time in my calculations :-)
– Archimedes
Nov 10 at 15:00
add a comment |
up vote
1
down vote
It is somewhat counterintuitive, but Mathematica might indeed think that A B Conjugate[A] Conjugate[B] is simpler.
LeafCount[Abs[A]^2 Abs[B]^2]
LeafCount[A B Conjugate[A] Conjugate[B]]
9
7
Notice that LeafCount is not the precise ComplexityFunction used by FullSimplify, but it may still give you an idea.
In the end, simplification is always a matter of taste.
answered Nov 10 at 11:51
Henrik Schumacher
46.8k466134
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
You can use ComplexExpand
simplify =
Simplify[ComplexExpand[#, Variables[Level[#, -1]],
TargetFunctions -> Abs, Arg]] &;
A*Conjugate[A] // simplify
(* Abs[A]^2 *)
simplify[A*Conjugate[A]*B*Conjugate[B]]
(* Abs[A]^2 Abs[B]^2 *)
answered Nov 10 at 13:33
Bob Hanlon
58.2k23594
Thank you. This will save a lot of time in my calculations :-)
– Archimedes
Nov 10 at 15:00
add a comment |
up vote
1
down vote
accepted
You can use ComplexExpand
simplify =
Simplify[ComplexExpand[#, Variables[Level[#, -1]],
TargetFunctions -> Abs, Arg]] &;
A*Conjugate[A] // simplify
(* Abs[A]^2 *)
simplify[A*Conjugate[A]*B*Conjugate[B]]
(* Abs[A]^2 Abs[B]^2 *)
answered Nov 10 at 13:33
Bob Hanlon
58.2k23594
Thank you. This will save a lot of time in my calculations :-)
– Archimedes
Nov 10 at 15:00
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
You can use ComplexExpand
simplify =
Simplify[ComplexExpand[#, Variables[Level[#, -1]],
TargetFunctions -> Abs, Arg]] &;
A*Conjugate[A] // simplify
(* Abs[A]^2 *)
simplify[A*Conjugate[A]*B*Conjugate[B]]
(* Abs[A]^2 Abs[B]^2 *)
answered Nov 10 at 13:33
Bob Hanlon
58.2k23594
You can use ComplexExpand
simplify =
Simplify[ComplexExpand[#, Variables[Level[#, -1]],
TargetFunctions -> Abs, Arg]] &;
A*Conjugate[A] // simplify
(* Abs[A]^2 *)
simplify[A*Conjugate[A]*B*Conjugate[B]]
(* Abs[A]^2 Abs[B]^2 *)
answered Nov 10 at 13:33
Bob Hanlon
58.2k23594
answered Nov 10 at 13:33
Bob Hanlon
58.2k23594
answered Nov 10 at 13:33
Bob Hanlon
58.2k23594
answered Nov 10 at 13:33
Bob Hanlon
58.2k23594
58.2k23594
Thank you. This will save a lot of time in my calculations :-)
– Archimedes
Nov 10 at 15:00
add a comment |
Thank you. This will save a lot of time in my calculations :-)
– Archimedes
Nov 10 at 15:00
Thank you. This will save a lot of time in my calculations :-)
– Archimedes
Nov 10 at 15:00
Thank you. This will save a lot of time in my calculations :-)
– Archimedes
Nov 10 at 15:00
add a comment |
up vote
1
down vote
It is somewhat counterintuitive, but Mathematica might indeed think that A B Conjugate[A] Conjugate[B] is simpler.
LeafCount[Abs[A]^2 Abs[B]^2]
LeafCount[A B Conjugate[A] Conjugate[B]]
9
7
Notice that LeafCount is not the precise ComplexityFunction used by FullSimplify, but it may still give you an idea.
In the end, simplification is always a matter of taste.
answered Nov 10 at 11:51
Henrik Schumacher
46.8k466134
add a comment |
up vote
1
down vote
It is somewhat counterintuitive, but Mathematica might indeed think that A B Conjugate[A] Conjugate[B] is simpler.
LeafCount[Abs[A]^2 Abs[B]^2]
LeafCount[A B Conjugate[A] Conjugate[B]]
9
7
Notice that LeafCount is not the precise ComplexityFunction used by FullSimplify, but it may still give you an idea.
In the end, simplification is always a matter of taste.
answered Nov 10 at 11:51
Henrik Schumacher
46.8k466134
add a comment |
up vote
1
down vote
up vote
1
down vote
It is somewhat counterintuitive, but Mathematica might indeed think that A B Conjugate[A] Conjugate[B] is simpler.
LeafCount[Abs[A]^2 Abs[B]^2]
LeafCount[A B Conjugate[A] Conjugate[B]]
9
7
Notice that LeafCount is not the precise ComplexityFunction used by FullSimplify, but it may still give you an idea.
In the end, simplification is always a matter of taste.
answered Nov 10 at 11:51
Henrik Schumacher
46.8k466134
It is somewhat counterintuitive, but Mathematica might indeed think that A B Conjugate[A] Conjugate[B] is simpler.
LeafCount[Abs[A]^2 Abs[B]^2]
LeafCount[A B Conjugate[A] Conjugate[B]]
9
7
Notice that LeafCount is not the precise ComplexityFunction used by FullSimplify, but it may still give you an idea.
In the end, simplification is always a matter of taste.
answered Nov 10 at 11:51
Henrik Schumacher
46.8k466134
answered Nov 10 at 11:51
Henrik Schumacher
46.8k466134
answered Nov 10 at 11:51
Henrik Schumacher
46.8k466134
answered Nov 10 at 11:51
Henrik Schumacher
46.8k466134
46.8k466134
add a comment |
add a comment |
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ComplexExpanddoes the work:A*Conjugate[A]*B*Conjugate[B] // ComplexExpand.– rmw
Nov 10 at 13:41
@rmw - You have let
ComplexExpandassume thatAandBare real-valued. The OP is working with complex variables.– Bob Hanlon
Nov 10 at 15:29