2. Law of subtraction: the subtraction of complex numbers is carried out according to the following rules: let z 1=a+bi and z2=c+di be any two complex numbers, then their difference is (a+bi)-(c+di) = (a-c)+(b-d) i.
3. Multiplication rule: it is stipulated that the multiplication of complex numbers should be carried out according to the following rules: let z 1=a+bi, z2=c+di(a, b, c, d∈R) be any two complex numbers, then their product (a+bi) (c+di) = (AC-BD).
4. Division rule: the definition of complex division: the complex number x+yi(x, y∈R) satisfying (c+di)(x+yi)=(a+bi) is the quotient of the complex number a+bi divided by the complex number c+di.
Application of complex numbers
system analysis
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 is located in the right half plane, the causal system is unstable; Located 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.