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

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  • 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




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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






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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?






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  • 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


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