Using Argument principle to find roots of complex polynomial. Studying for qualifying exam

I know we need to use the argument principle to solve this, but I don’t know how to use this.

Argument Principle states: $$
text{number of zeros}=frac{1}{2pi i}int_{partialOmega}frac{f'(z)}{f(z)}dz.
$$
Here
$$
partialOmega={z=iy, -Rleq yleq R}cup{ z=Re^{itheta},-frac{pi}{2}leq thetaleqfrac{pi}{2}}.
$$
It claims that
$$
int_{-iR}^{iR}frac{f'(z)}{f(z)}dz=0.
$$

I need to find the number of zeros in the first quadrant. This is a problem for my qualifying exam practice. I found it in Nakhle’s complex analysis for applications, and I am not understanding how to apply this theorem. Any ideas on how to proceed or solve this would be greatly appreciated.

The function is $$ f(z) = z^5 + z^4 + 4z^3 + 10z^2 + 9$$