Sketch for both conditions.

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Solution:-a) GivenG(s)=\frac{k}{s(s+2)(s+1+j)(s+1-j)}The centre of asymptotes is\begin{array}{l}\sigma_{c}=-\frac{(0+2+1+j+1-j)}{4} \\\sigma_{c}=-1\end{array}For k>0, the angles of the asymptotes are\theta=45^{\circ}, 135^{\circ}, 225^{\circ} \& 135^{\circ}For k<0, the angles of the asymptotes are\theta=0^{\circ}, 90^{\circ}, 180^{\circ} \& 270^{\circ}SketchFor K \geq 0for \quad K<0b) Cniven charectesiscs equation\begin{array}{l} s(s+2)(s+3)+k=0 \\\Rightarrow \quad 1+\frac{k}{s(s+2)(s+3)}=0 \\\text { so centroid }=\frac{(0-2-3)-0}{3-0} \\=-1.67\end{array}So the asymptotes will cut x-axis at -1.67Thanks ...