A number in the form of z = A+bi(A and B are both real numbers) is called a complex number, where A is called the real part, B is called the imaginary part, and I is called the imaginary part. When the imaginary part of z is equal to zero, z is often called a real number; When the imaginary part of z is not equal to zero and the real part is equal to zero, z is often called pure imaginary number. Complex number field is an algebraic closure of real number field, that is, any polynomial with complex coefficients always has roots in complex number field. Complex number was first put forward by Cardan, a scholar in Milan, Italy, in the16th century. Through the work of D'Alembert, De Moivre, Euler and Gauss, this concept was gradually accepted by mathematicians.

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In system analysis, Laplace transform is often used to transform the system from time domain to frequency domain. Therefore, the poles and zeros of the system can be analyzed on the complex plane. The root locus method, Nyquist diagram method and Nicholstu method for analyzing the stability of the system are all carried out on the complex plane.

Whether the poles and zeros of the system are in the left half plane or the right half plane, the root locus method is very important. If the system pole

Located in the right half plane, the causal system is unstable; If they all lie in the left half plane, the causal system is stable; On the imaginary axis, the system is critically stable. If all zeros and poles of the system are in the left half plane, it is the minimum phase system. A system is all-pass if its poles and zeros are symmetrical about the imaginary axis.