Revisions to Conjugation with real elements

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edited Feb 9, 2021 at 5:17

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Using ComplexExpand command:

A = 5 t^2 + 3 t + 4;
ComplexExpand[Conjugate[A]]

For expressions within radicals, we must use the Refine command for the ComplexExpand command to work properly. Here is an example:

Without Refine command:

 In[]:= Simplify[ComplexExpand[Conjugate[Sqrt[a - b c]]]]
Out[]:= (*((a - b c)^2)^(1/4) (Cos[1/2 Arg[a - b c]] - I Sin[1/2 Arg[a - b c]])*)

With Refine command for $a-bc>0$ or $a-bc<0$

 In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], Assumptions -> a - b c > 0]
Out[]:= Sqrt[a(*Sqrt[a - b c]c]*)

 In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], Assumptions -> a - b c < 0]
Out[]:= (*- I*Sqrt[b c - a]a]*)

Using ComplexExpand command:

A = 5 t^2 + 3 t + 4;
ComplexExpand[Conjugate[A]]

For expressions within radicals, we must use the Refine command for the ComplexExpand command to work properly. Here is an example:

Without Refine command:

 In[]:= Simplify[ComplexExpand[Conjugate[Sqrt[a - b c]]]]
Out[]:= ((a - b c)^2)^(1/4) (Cos[1/2 Arg[a - b c]] - I Sin[1/2 Arg[a - b c]])

With Refine command for $a-bc>0$ or $a-bc<0$

 In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], Assumptions -> a - b c > 0]
Out[]:= Sqrt[a - b c]

 In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], Assumptions -> a - b c < 0]
Out[]:= - I*Sqrt[b c - a]

Using ComplexExpand command:

A = 5 t^2 + 3 t + 4;
ComplexExpand[Conjugate[A]]

For expressions within radicals, we must use the Refine command for the ComplexExpand command to work properly. Here is an example:

Without Refine command:

 Simplify[ComplexExpand[Conjugate[Sqrt[a - b c]]]]
 (*((a - b c)^2)^(1/4) (Cos[1/2 Arg[a - b c]] - I Sin[1/2 Arg[a - b c]])*)

With Refine command for $a-bc>0$ or $a-bc<0$

 Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], Assumptions -> a - b c > 0]
 (*Sqrt[a - b c]*)

 Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], Assumptions -> a - b c < 0]
 (*- I*Sqrt[b c - a]*)

deleted 7 characters in body

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edited Feb 7, 2021 at 2:39

E. Chan-López

31.2k
3
29
50

Using ComplexExpand command:

A = 5 t^2 + 3 t + 4;
ComplexExpand[Conjugate[A]]

For expressions within radicals, we must use the Refine command for the ComplexExpand command to work properly. Here is an example:

Without Refine command:

 In[]:= Simplify[ComplexExpand[Conjugate[Sqrt[a - b c]]]]
Out[]:= ((a - b c)^2)^(1/4) (Cos[1/2 Arg[a - b c]] - I Sin[1/2 Arg[a - b c]])

With RefineRefine command for $a-bc>0$ or $a-bc<0$

 In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], 
 Assumptions -> a - b c > 0]
Out[]:= Sqrt[a - b c]

 In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], 
 Assumptions -> a - b c < 0]
Out[]:= - I*Sqrt[b c - a]

Using ComplexExpand command:

A = 5 t^2 + 3 t + 4;
ComplexExpand[Conjugate[A]]

For expressions within radicals, we must use the Refine command for the ComplexExpand command to work properly. Here is an example:

Without Refine command:

 In[]:= Simplify[ComplexExpand[Conjugate[Sqrt[a - b c]]]]
Out[]:= ((a - b c)^2)^(1/4) (Cos[1/2 Arg[a - b c]] - I Sin[1/2 Arg[a - b c]])

With Refine command for $a-bc>0$ or $a-bc<0$

 In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], 
 Assumptions -> a - b c > 0]
Out[]:= Sqrt[a - b c]

In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], 
 Assumptions -> a - b c < 0]
Out[]:= - I*Sqrt[b c - a]

Using ComplexExpand command:

A = 5 t^2 + 3 t + 4;
ComplexExpand[Conjugate[A]]

For expressions within radicals, we must use the Refine command for the ComplexExpand command to work properly. Here is an example:

Without Refine command:

 In[]:= Simplify[ComplexExpand[Conjugate[Sqrt[a - b c]]]]
Out[]:= ((a - b c)^2)^(1/4) (Cos[1/2 Arg[a - b c]] - I Sin[1/2 Arg[a - b c]])

With Refine command for $a-bc>0$ or $a-bc<0$

 In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], Assumptions -> a - b c > 0]
Out[]:= Sqrt[a - b c]

 In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], Assumptions -> a - b c < 0]
Out[]:= - I*Sqrt[b c - a]

added 631 characters in body

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edited Feb 7, 2021 at 2:31

E. Chan-López

31.2k
3
29
50

Using ComplexExpand command:

A = 5 t^2 + 3 t + 4;
ComplexExpand[Conjugate[A]]

For expressions within radicals, we must use the Refine command for the ComplexExpand command to work properly. Here is an example:

Without Refine command:

 In[]:= Simplify[ComplexExpand[Conjugate[Sqrt[a - b c]]]]
Out[]:= ((a - b c)^2)^(1/4) (Cos[1/2 Arg[a - b c]] - I Sin[1/2 Arg[a - b c]])

With Refine command for $a-bc>0$ or $a-bc<0$

 In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], 
Assumptions -> a - b c > 0]
Out[]:= Sqrt[a - b c]

In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], 
Assumptions -> a - b c < 0]
Out[]:= - I*Sqrt[b c - a]

Using ComplexExpand command:

A = 5 t^2 + 3 t + 4;
ComplexExpand[Conjugate[A]]

Using ComplexExpand command:

A = 5 t^2 + 3 t + 4;
ComplexExpand[Conjugate[A]]

For expressions within radicals, we must use the Refine command for the ComplexExpand command to work properly. Here is an example:

Without Refine command:

 In[]:= Simplify[ComplexExpand[Conjugate[Sqrt[a - b c]]]]
Out[]:= ((a - b c)^2)^(1/4) (Cos[1/2 Arg[a - b c]] - I Sin[1/2 Arg[a - b c]])

With Refine command for $a-bc>0$ or $a-bc<0$

 In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], 
Assumptions -> a - b c > 0]
Out[]:= Sqrt[a - b c]

In[]:= Refine[ComplexExpand[Conjugate[Sqrt[a - b c]]], 
Assumptions -> a - b c < 0]
Out[]:= - I*Sqrt[b c - a]

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created Feb 6, 2021 at 21:47

E. Chan-López

31.2k
3
29
50

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