# Math Help - roots of z tan z

1. ## roots of z tan z

hello, can someone please show me how the roots of z tan z = k , where k > 0 are real is solved.

what i have done; z tan z = $z * \frac{sinz}{cosz}$

by Euler equations $(x+iy) * \frac{e^i^z- e^-^i^z}{2i} / \frac{e^i^z + e^-^i^z}{2}$

$(x+iy) * \frac{e^i^z- e^-^i^z}{2i} / \frac{e^i^z + e^-^i^z}{2}$

$(x+iy) * \frac{e^i^z - e^-^i^z} { i(e^i^z + e^-^i^z)}$

would appreciate some help solving this thanks guys

2. ## Re: roots of z tan z

The first thing I would do is get the denominator real by multiplying numerator and denominator by the conjugate, -i (note that eiz+ e[sup]-iz[/itex] is a real number because it is equal to its conjugate).