Can anyone explain me why the breakaway points in Root-Locus are only on the real axis?
2026-03-27 21:23:28.1774646608
Breakaway Point in Root-Locus
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Root locus is the graphical representation of the evolution of the characteristic equation. i.e. it shows how the roots vary as you vary the value of $k$.
Coming to roots of the characteristic equation, which is a polynomial, we know that they are either real or occur in complex conjugates. i.e of the form $x \pm iy$. And further, the roots depend continuously on the value of $k$.
Hence, as we vary $k$, the only possibility for break away is when we travel on the real axis (roots are real) and then break away (roots become complex in conjugate pairs).