The task is to find number of $ {z^4} + {z^3} - 4z + 1 = 0$ in the area $1 < \left| z \right| < 2$. (this task is in the Rouché's theorem paragraph)
I used this theorem many times, but I don't know to solve this task. This is simple to find number of roots in the area $0 < \left| z \right| < 1$, but I don't know how to do the same in another area: $0 < \left| z \right| < 2$.
Of course, I now number of roots with the help of Wolfram Alpha, for example.
Could you help, please, how to solve this task with the Rouché's theorem?