The mathematical analysis - an obligatory subject for students of technical colleges of Russia. One of the most difficult subjects of the first semester for most of students is the solution of complex numbers. Meanwhile, by close examination of complex numbers, it becomes clear that their decision is reached by means of enough simple algorithms.
It is required to you
- Grant according to the mathematical analysis
Instruction
1. Complex numbers are used for expansion of a set of real numbers. If real numbers can be presented graphically on a coordinate line, then to represent complex number, two coordinate axes (abscissae and ordinates) will be required. Complex numbers can be received in that case, for example, if at a quadratic equation the discriminant is less than zero.
2. Any complex number it is possible to present in the form x+yi sums where number x is a material part of complex number c, and number y - imaginary. The symbol i in this case is called imaginary unit, it is equal to a square root from minus units (in real numbers the operation of extraction of a root from a negative number is forbidden).
3. To make operation of addition (subtraction) over couple of complex numbers, it is enough to remember the simple rule: material parts develop separately, imaginary separately. That is: (x1+y1*i)+ (x2+y2*i)= (x1+x2)+ (y1+y2) of *i.
4. It is much more difficult to multiply and divide complex numbers, than to put and read, but as a result everything comes down to trivial formulas. These formulas are presented in the drawing and received by means of usual algebraic transformations taking into account that it is necessary to put complex numbers in parts, and the square of imaginary unit is equal to negative unit.
5. Sometimes in tasks it is required to calculate the module of complex number. It is easy to make it. It is necessary to take a square root from the sum of a material and imaginary part of complex number. It will also be numerical value of the module of complex number.