Question

what is tan(x+iy) in term of x and y help pls

Answer 1

WoAh!!!
Is the a angle a complex number?? :O

Answer 2

http://espanol.answers.yahoo.com/question/index?qid=20090311051640AAIUbNJ

Answer 3

or look for hyperbolic identitys

Answer 4

\[\tan(x+iy)=\frac{ \tan(x)+\tan(iy) }{ 1-\tan(x)\tan(iy) }\]You can leave it this way or elaborate a little more:\[\tan(iy)=\frac{ \sin(iy) }{ \cos(iy) }=-i \frac{ e^{i(iy)}-e^{-i(iy)} }{ e^{i(iy)}+e^{-i(iy)} }=i \frac{ e^y-e^{-y} }{ e^y+e^{-y} }=iTh(y)\]then \[\tan(x+iy)=\frac{ \tan(x)+iTh(y) }{ 1-itan(x)Th(y) }\]

Answer 5

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