1. Addition: When two complex numbers are added, the real part and the real part are added, and the imaginary part and the imaginary part are added. For example, (3+2i)+( 1+4i)=4+6i.
2. Subtraction: When two complex numbers are subtracted, the real part and imaginary part are subtracted. For example, (3+2i)-( 1+4i)=2-2i.
3. Multiplication: When two complex numbers are multiplied, they follow the distribution law and the combination law. For example, (3+2i) (1+4i) = (3 *1-2 * 4)+(3 * 4+2 *1) i =-5+10i.
4. Division: When two complex numbers are divided, the result is a complex number. For example, (3+2i)/(1+4i) = ((3 *1+2 * 4) i-(3 * 4+2 *1))/(12+42) =
5. modulus: the modulus of a complex number is the distance from the origin, which is expressed by r and satisfies R 2 = A 2+B 2. For example, | 3+2i | = sqrt (9+4) = sqrt (13).
6. * * * York complex number: The * * * York complex number of a complex number is a complex number obtained by inverting the imaginary part. For example, the complex number of * * * yoke of (3+2i) is (3-2i).
7. Power operation: the power operation of a complex number can be regarded as the result of power operation of the real part and the imaginary part respectively. For example, (3+2i) 2 = (3 2-2 2)+2 * 3 * 2i = 8-4i.
8. Logarithmic operation: the natural logarithm of a complex number is the result of natural logarithm operation on its real part and imaginary part respectively. For example, log (3+2i) = log (3)+log (2i) = log (3)+log (-1/2) * i.
The above are the main operation rules of complex numbers. It should be noted that due to the complexity of complex numbers, these operations usually need to be simplified and calculated by tools such as Euler formula.