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Math Help - real and imaginary parts of tan(z)

  1. #1
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    real and imaginary parts of tan(z)

    Hi, firstly i am confused as to what tan(z) is. Is it just tan(x+iy) and how do i find the real and imaginary parts of it? From this how do i find the solutions to tan(z) = 0?
    Thanks.
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  2. #2
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    Quote Originally Posted by Roxanne123456789 View Post
    Hi, firstly i am confused as to what tan(z) is. Is it just tan(x+iy) and how do i find the real and imaginary parts of it? From this how do i find the solutions to tan(z) = 0?
    Thanks.


    \tan z=\frac{\sin z}{\cos z}\,,\,\sin z=\frac{e^x-e^{-z}}{2i}\,,\,\cos z=\frac{e^z+e^{-z}}{2}

    Now do some algebra (for example, multiplying the whole thing by \frac{e^z}{e^z} and...

    Tonio
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  3. #3
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    Could i not just use sin(z)=sin(x+iy) so Re(sin(z))= sin(x)cosh(y) and Im(sin(z)) = cos(x)sinh(y) and do the same for cos(x+iy) and then find the real and imaginary parts of tan(z) that way?
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