Question

find the domain
R(z)=5 / (z^3+10z^2+9z)

Answer 1

If you look at the expression \[R(z)=\frac{5}{z^3+10z^2+9z}\] then you can see the only case when something goes wrong is if you divide by zero so you just have to find where is the denominator zero. The domain will contain any other point of the complex plane.

Solution: \[z^3+10z^2+9z=z(z^2+10z+9)=z(z+1)(z+9)=0\Longrightarrow\]\[ z=0 \vee z=-1\vee z=-9.\] So \[D_R=\mathbb{C}\backslash\{0;-1;-9\}.\]

Answer 2

thanx