A unity feedback control system has an open-loop transfer function $$$G\left(s\right)=\frac K{s\left(s^2+7s+12\right)}$$$ The gain K for which s = −1 + j1 will lie on the root locus of this system is:

A unity feedback system is given as,$$$G\left(s\right)=\frac{K\left(1-s\right)}{s\left(s+3\right)}$$$ indicate the correct root locus diagram.

The root locus of the system $$$G\left(s\right)H\left(s\right)=\frac K{s\left(s+2\right)\left(s+3\right)}$$$ has the break-away point located at

Consider the points s₁ = −3 + j4 and s₂ = −3 − j2 in the s-plane. Then, for a system with the open loop transfer function $$$G\left(s\right)H\left(s\right)=\frac K{\left(s+1\right)^4}$$$