I'm doing a trivial mistake for sure, but I struggling to find it...
I have: $$ \frac{160}{4s^2+4.8s+4} = \frac{160}{(s+0.6-0.8i)(s+0.6+0.8i)} = \frac{K_1}{s+0.6-0.8i} +\frac{K_1^*}{s+0.6+0.8i} $$$$ K_1= -100i $$
but if I first multiply by $\frac{1}{4}$, I get: $$ \frac{40}{s^2+1.2s+1} = \frac{40}{(s+0.6-0.8i)(s+0.6+0.8i)} = \frac{K_1}{s+0.6-0.8i} +\frac{K_1^*}{s+0.6+0.8i} $$$$ K_1= -25i $$
I know the second expression is the right one. So what I'm I missing in the first one?
If roots of a quadratic equation are $\alpha$ and $\beta$ then for an equation with leading coefficient 1: $$f(x)=x^2+bx+b=(x-\alpha)(x-\beta)\quad\text{where }f(\alpha)=f(\beta)=0$$ But not for this but instead: $$f_2(x)=ax^2+abx+ac\begin{cases}\ne(x-\alpha)(x-\beta)\\=a(x-\alpha)(x-\beta)\end{cases}\quad\text{where }f(\alpha)=f(\beta)=0$$