I have the following function $F(s)=\frac{1}{(s+10)(1-s)}$ and need to find the real axis and imaginary axis intercepts when $s=j\omega$.
I tried by splitting $F(j\omega)=\frac{1}{(j\omega+10)(1-j\omega)}$ into real and imaginary parts and got
$Re[F(j\omega)]=\frac{\omega^2+10}{\omega^4+101\omega^2+100}$
$Im[F(j\omega)]=\frac{9\omega}{\omega^4+101\omega^2+100}$
When I solve $\frac{\omega^2+10}{\omega^4+101\omega^2+100}=0$ for $\omega$ I get $\omega=\pm\:j\sqrt{10}$
Now replacing $\omega$ in $\frac{9\omega}{\omega^4+101\omega^2+100}$ with $\sqrt{10}$ and I get $-\frac{j}{9\sqrt(10)}$ when I would expect a real number in order to define the j intercept.