Complex sizes are mathematical abstraction. They were entered with the purpose to facilitate understanding of some processes. They can very often be met in textbooks by mathematics and physics.
The general concept about complex number
If you need to call distance between two cities, then it is possible to give the answer consisting of one number in miles, kilometers or in other units of measure of linear distances. However if you have to describe how to reach from one city another, then it is necessary to give more information, than just distance between two points on the map. In this case It is necessary to tell about the direction in which it is necessary to move also about time of the movement.
The type of information which expresses one-dimensional measurement in science is called scalar size. Scalars are the numbers used in the majority of mathematical calculations. For example, the weight and speed which are possessed by any given object are scalar sizes.
Successfully to analyze the natural phenomena, we have to work with the abstract objects and methods capable to represent multidimensional sizes. Here it is necessary to refuse scalar numbers in favor of complex. They give the chance to express two measurements at the same time. It is easier to understand complex numbers when they are presented in the graphic form. If to draw the line having a certain length and the direction, then it also will be graphical representation of complex number. It is also widely known in physics as a vector.
Differences between complex and scalar sizes
Such types of numbers as whole, rational, irrational and real are familiar to children from school. The one-dimensionality is inherent in all of them. Straightforwardness of a numerical straight line illustrates it graphically. You can be moved up or down it, but all "movements" on this line will be are limited to a horizontal axis. One-dimensional, scalar figures are quite enough for calculation of quantity of objects, expression of weight or measurement of constant tension of the battery. But they cannot designate something more difficult. Scalars it is impossible to express at the same time distance and the direction between two cities, or amplitude with a phase. It is necessary to present these types of numbers already in the form of multidimensional area of values. In other words, we need vector sizes which can have not only the size, but also the direction of distribution.
Conclusion
The scalar number is type of a mathematical object which people got used to use in everyday life is the temperature, length, weight, etc. The complex number represents value which includes two types of data. The vector is the graphic representation of complex number. It looks as an arrow with the initial point determined by length and the direction. Sometimes the word "vector" is used in radio engineering where it expresses phase shift between signals.