Let the complex number z=a+bi(a, b∈R), and its geometric meaning is the distance from a point (a, b) on the complex plane to the origin.

Algorithm:

| z 1 z2| = |z 1| |z2|

┃| z 1 |-| z2|┃≤| z 1+z2 |≤| z 1 |+| z2 |

| z1| z1-z2 | =| z1z2 || is the formula of the distance between two points on the complex plane, from which the equations of lines, circles, hyperbolas, ellipses and parabolas on the complex plane can be derived.

Extended data:

algorithm

1, addition rule

The addition rule of complex numbers: let z 1=a+bi and z2=c+di be any two complex numbers. The real part of sum is the sum of the original two complex real parts, and its imaginary part is the sum of the original two imaginary parts. The sum of two complex numbers or a complex number.

2, the law of multiplication

Complex multiplication rule: two complex numbers are multiplied, similar to two polynomials. In the result, i2=-1, and the real part and imaginary part are merged respectively. The product of two complex numbers is still a complex number.