Complex analysis… I can't write the function $f(z) =tan (z)$ as a real part and imaginary part [duplicate]

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite













This question already has an answer here:



  • Real and Imaginary Parts of tan(z)

    2 answers




How to write the function $f(z) =tan (z)$ as a real part and imaginary part?




I have reached the form :
beginalign
tan (z) &= fracsin(z)cos(z)\
&= frace^iz - e^-iz i (e^iz+ e^-iz)
endalign




complex-analysis trigonometry




share|cite|improve this question













marked as duplicate by amWhy, Robert Z, user 108128, David K, anomaly Jul 28 at 13:33


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.














  • I'm a new user & I have not read all question below... sorry!
    – Momen Nawafleh
    Jul 28 at 13:40














up vote
0
down vote

favorite













This question already has an answer here:



  • Real and Imaginary Parts of tan(z)

    2 answers




How to write the function $f(z) =tan (z)$ as a real part and imaginary part?




I have reached the form :
beginalign
tan (z) &= fracsin(z)cos(z)\
&= frace^iz - e^-iz i (e^iz+ e^-iz)
endalign




complex-analysis trigonometry




share|cite|improve this question













marked as duplicate by amWhy, Robert Z, user 108128, David K, anomaly Jul 28 at 13:33


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.














  • I'm a new user & I have not read all question below... sorry!
    – Momen Nawafleh
    Jul 28 at 13:40












up vote
0
down vote

favorite









up vote
0
down vote

favorite












This question already has an answer here:



  • Real and Imaginary Parts of tan(z)

    2 answers




How to write the function $f(z) =tan (z)$ as a real part and imaginary part?




I have reached the form :
beginalign
tan (z) &= fracsin(z)cos(z)\
&= frace^iz - e^-iz i (e^iz+ e^-iz)
endalign




complex-analysis trigonometry




share|cite|improve this question














This question already has an answer here:



  • Real and Imaginary Parts of tan(z)

    2 answers




How to write the function $f(z) =tan (z)$ as a real part and imaginary part?




I have reached the form :
beginalign
tan (z) &= fracsin(z)cos(z)\
&= frace^iz - e^-iz i (e^iz+ e^-iz)
endalign





This question already has an answer here:



  • Real and Imaginary Parts of tan(z)

    2 answers





complex-analysis trigonometry





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 28 at 13:01









José Carlos Santos

112k1696173




112k1696173









asked Jul 28 at 12:35









Momen Nawafleh

61




61




marked as duplicate by amWhy, Robert Z, user 108128, David K, anomaly Jul 28 at 13:33


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.






marked as duplicate by amWhy, Robert Z, user 108128, David K, anomaly Jul 28 at 13:33


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.













  • I'm a new user & I have not read all question below... sorry!
    – Momen Nawafleh
    Jul 28 at 13:40
















  • I'm a new user & I have not read all question below... sorry!
    – Momen Nawafleh
    Jul 28 at 13:40















I'm a new user & I have not read all question below... sorry!
– Momen Nawafleh
Jul 28 at 13:40




I'm a new user & I have not read all question below... sorry!
– Momen Nawafleh
Jul 28 at 13:40










1 Answer
1






active

oldest

votes

















up vote
4
down vote













If $x,yinmathbb R$, thenbeginaligntan(x+yi)&=fractan(x)+tan(yi)1-tan(x)tan(yi)\&=fractan(x)+itanh(y)1-itan(x)tanh(y)\&=fracbigl(tan(x)+itanh(y)bigr)bigl(1+itan(x)tanh(y)bigr)1+tan^2(x)tanh^2(y).endalignCan you do the rest?






share|cite|improve this answer





















  • I don't understand what did you do ..!
    – Momen Nawafleh
    Jul 28 at 13:22










  • Can you interpret more than above?
    – Momen Nawafleh
    Jul 28 at 13:23











  • It's up to you to tell me what is it that you don't understand.
    – José Carlos Santos
    Jul 28 at 13:25










  • At the first step ; how do you divide by (1-tan(x) tan (iy)) ?
    – Momen Nawafleh
    Jul 28 at 13:28






  • 1




    @MomenNawafleh You only need to type the formulas enclosed in $ signs. The website replaces the content with the image of the formula. For example, if you type $tan(x)=fracsin(x)cos(x)$, it will get replaced by $tan(x)=fracsin(x)cos(x)$
    – user578878
    Jul 28 at 15:05

















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
4
down vote













If $x,yinmathbb R$, thenbeginaligntan(x+yi)&=fractan(x)+tan(yi)1-tan(x)tan(yi)\&=fractan(x)+itanh(y)1-itan(x)tanh(y)\&=fracbigl(tan(x)+itanh(y)bigr)bigl(1+itan(x)tanh(y)bigr)1+tan^2(x)tanh^2(y).endalignCan you do the rest?






share|cite|improve this answer





















  • I don't understand what did you do ..!
    – Momen Nawafleh
    Jul 28 at 13:22










  • Can you interpret more than above?
    – Momen Nawafleh
    Jul 28 at 13:23











  • It's up to you to tell me what is it that you don't understand.
    – José Carlos Santos
    Jul 28 at 13:25










  • At the first step ; how do you divide by (1-tan(x) tan (iy)) ?
    – Momen Nawafleh
    Jul 28 at 13:28






  • 1




    @MomenNawafleh You only need to type the formulas enclosed in $ signs. The website replaces the content with the image of the formula. For example, if you type $tan(x)=fracsin(x)cos(x)$, it will get replaced by $tan(x)=fracsin(x)cos(x)$
    – user578878
    Jul 28 at 15:05














up vote
4
down vote













If $x,yinmathbb R$, thenbeginaligntan(x+yi)&=fractan(x)+tan(yi)1-tan(x)tan(yi)\&=fractan(x)+itanh(y)1-itan(x)tanh(y)\&=fracbigl(tan(x)+itanh(y)bigr)bigl(1+itan(x)tanh(y)bigr)1+tan^2(x)tanh^2(y).endalignCan you do the rest?






share|cite|improve this answer





















  • I don't understand what did you do ..!
    – Momen Nawafleh
    Jul 28 at 13:22










  • Can you interpret more than above?
    – Momen Nawafleh
    Jul 28 at 13:23











  • It's up to you to tell me what is it that you don't understand.
    – José Carlos Santos
    Jul 28 at 13:25










  • At the first step ; how do you divide by (1-tan(x) tan (iy)) ?
    – Momen Nawafleh
    Jul 28 at 13:28






  • 1




    @MomenNawafleh You only need to type the formulas enclosed in $ signs. The website replaces the content with the image of the formula. For example, if you type $tan(x)=fracsin(x)cos(x)$, it will get replaced by $tan(x)=fracsin(x)cos(x)$
    – user578878
    Jul 28 at 15:05












up vote
4
down vote










up vote
4
down vote









If $x,yinmathbb R$, thenbeginaligntan(x+yi)&=fractan(x)+tan(yi)1-tan(x)tan(yi)\&=fractan(x)+itanh(y)1-itan(x)tanh(y)\&=fracbigl(tan(x)+itanh(y)bigr)bigl(1+itan(x)tanh(y)bigr)1+tan^2(x)tanh^2(y).endalignCan you do the rest?






share|cite|improve this answer













If $x,yinmathbb R$, thenbeginaligntan(x+yi)&=fractan(x)+tan(yi)1-tan(x)tan(yi)\&=fractan(x)+itanh(y)1-itan(x)tanh(y)\&=fracbigl(tan(x)+itanh(y)bigr)bigl(1+itan(x)tanh(y)bigr)1+tan^2(x)tanh^2(y).endalignCan you do the rest?







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Jul 28 at 12:45









José Carlos Santos

112k1696173




112k1696173











  • I don't understand what did you do ..!
    – Momen Nawafleh
    Jul 28 at 13:22










  • Can you interpret more than above?
    – Momen Nawafleh
    Jul 28 at 13:23











  • It's up to you to tell me what is it that you don't understand.
    – José Carlos Santos
    Jul 28 at 13:25










  • At the first step ; how do you divide by (1-tan(x) tan (iy)) ?
    – Momen Nawafleh
    Jul 28 at 13:28






  • 1




    @MomenNawafleh You only need to type the formulas enclosed in $ signs. The website replaces the content with the image of the formula. For example, if you type $tan(x)=fracsin(x)cos(x)$, it will get replaced by $tan(x)=fracsin(x)cos(x)$
    – user578878
    Jul 28 at 15:05
















  • I don't understand what did you do ..!
    – Momen Nawafleh
    Jul 28 at 13:22










  • Can you interpret more than above?
    – Momen Nawafleh
    Jul 28 at 13:23











  • It's up to you to tell me what is it that you don't understand.
    – José Carlos Santos
    Jul 28 at 13:25










  • At the first step ; how do you divide by (1-tan(x) tan (iy)) ?
    – Momen Nawafleh
    Jul 28 at 13:28






  • 1




    @MomenNawafleh You only need to type the formulas enclosed in $ signs. The website replaces the content with the image of the formula. For example, if you type $tan(x)=fracsin(x)cos(x)$, it will get replaced by $tan(x)=fracsin(x)cos(x)$
    – user578878
    Jul 28 at 15:05















I don't understand what did you do ..!
– Momen Nawafleh
Jul 28 at 13:22




I don't understand what did you do ..!
– Momen Nawafleh
Jul 28 at 13:22












Can you interpret more than above?
– Momen Nawafleh
Jul 28 at 13:23





Can you interpret more than above?
– Momen Nawafleh
Jul 28 at 13:23













It's up to you to tell me what is it that you don't understand.
– José Carlos Santos
Jul 28 at 13:25




It's up to you to tell me what is it that you don't understand.
– José Carlos Santos
Jul 28 at 13:25












At the first step ; how do you divide by (1-tan(x) tan (iy)) ?
– Momen Nawafleh
Jul 28 at 13:28




At the first step ; how do you divide by (1-tan(x) tan (iy)) ?
– Momen Nawafleh
Jul 28 at 13:28




1




1




@MomenNawafleh You only need to type the formulas enclosed in $ signs. The website replaces the content with the image of the formula. For example, if you type $tan(x)=fracsin(x)cos(x)$, it will get replaced by $tan(x)=fracsin(x)cos(x)$
– user578878
Jul 28 at 15:05




@MomenNawafleh You only need to type the formulas enclosed in $ signs. The website replaces the content with the image of the formula. For example, if you type $tan(x)=fracsin(x)cos(x)$, it will get replaced by $tan(x)=fracsin(x)cos(x)$
– user578878
Jul 28 at 15:05


Comments

Post a Comment

Popular posts from this blog

What is the equation of a 3D cone with generalised tilt?

Image
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that most of them have their point at the origin $(0,0,0)$ - I was wondering if anyone could give me a more generalized cone equation for a cone in any position in 3D space 3d share | cite | improve this question edited Jul 25 '16 at 0:05 ervx 9,425 3 13 36 asked Jul 24 '16 at 15:38 Charlene 11 2 2 Welcome to Math.SE! Could you please explain a few things to help people give an answer useful to you: 1. What do you mean by "generalized tilt"? 2. Are you asking about a right circular cone? Does the angle at the vertex matter? 3. What form of answer (implicit, parametric...?) are you looking for? 4. If this is homework, what tools do you have available, an
Read more

Color the edges and diagonals of a regular polygon

Image
Clash Royale CLAN TAG #URR8PPP up vote 5 down vote favorite 1 Here is the problem: For what $n$ is it possible to color the edges and diagonals of an $n$-side regular polygon with $dfracbinomn23$ colors, such that you use every color exactly three times and for every color the three segments (edges or diagonals) with that color form a triangle? Trivially $nequiv 0 text or 1 pmod3$. I can also prove that if the statement is true for $k$ than it is true for $3k$ as well. How to finish? Please help! Thanks combinatorial-geometry share | cite | improve this question edited Aug 6 at 21:57 alcana 118 4 asked Aug 6 at 21:15 Leo Gardner 356 11 Even assuming "polyhpn" in the title is a typo for polygon , it is unclear what you mean by "the edges and sides". Aren't the side of a regular polygon the same as the edges? A regular $n$-sided polygon has $n$ edges. – hardmath Aug 6 at 21:20 3 $n$ ne
Read more

Relationship between determinant of matrix and determinant of adjoint?

Image
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite We are studying adjoints in class, and I was curious if there is a relationship between the determinant of matrix A, and the determinant of the adjoint of matrix A? I assume there would be a relationship because finding the adjoint requires creating a cofactor matrix and then transposing it. linear-algebra determinant adjoint-operators share | cite | improve this question asked Nov 17 '17 at 17:32 CluelessCoder 32 5 For a square matrix $A$ of order $n$, we have $A(operatornameadj A)=(operatornameadj A)A=|A|I_n$ where $I_n$ is the identity matrix of order $n$. This should tell you about the determinant of the adjoint in terms of that of $A$ (use multiplicative property and other elementary properties of determinants). – Prasun Biswas Nov 17 '17 at 17:35 1 @CluelessCoder: see here: math.stackexchange.com/questions/516127/… – Hector Blandin Nov 17 &
Read more