The imaginary number is a number in the form of a+b*i, where a and b are real numbers, and b≠0, i? = - 1。 The value of the positive square root of the sum of the squares of the real and imaginary parts of a complex number is called the module of the complex number.

Let the complex number z=a+bi(a, b∈R), then the module of the complex number z |z|=√a? +b？ Its geometric meaning is the distance from a point (a, b) on the complex plane to the origin.

brief introduction

The word imaginary number was founded by Descartes, a famous mathematician in the17th century, because the concept at that time thought it was a non-existent real number. Later, it was found that the real part A of the imaginary number a+b*i can correspond to the horizontal axis and the imaginary part B can correspond to the vertical axis on the plane, so that the imaginary number a+b*i can correspond to the points (a, b) on the plane.

The imaginary number bi can be added to the real number A to form a complex number in the form of a+bi, where the real numbers A and B are called the real part and imaginary part of the complex number respectively. Some authors use the term pure imaginary number to represent the so-called imaginary number, which refers to any complex number whose imaginary part is not zero.