You will need

- Handbook on mathematical analysis

Instruction

1

Complex

**numbers**are used to extend the set of real numbers. If the real**numbers**can graphically represent on the coordinate axis, in order to represent a complex number would require two coordinate axes (abscissa and ordinate). Complex**numbers**can be obtained in the case, for example, if the quadratic equation discriminant is less than zero.2

Any complex number can be represented as a sum x+yi, where x is real part of complex

**number**c and a number y is the imaginary. The character i in this case is called the imaginary unit, it is equal to the square root of minus one (in real**numbers**x, the operation of extracting the square root of negative**numbers**is forbidden).3

To perform the operation of addition (subtraction) on two complex numbers, just remember a simple rule: real parts are added separately, imaginary separately. That is:

(x1+y1*i)+(x2+y2*i)=(x1+x2)+(y1+y2)*i.

(x1+y1*i)+(x2+y2*i)=(x1+x2)+(y1+y2)*i.

4

Multiply and divide complex

**numbers**much more complicated than add and subtract, but in the end it all comes down to trivial formulas. These formulas are presented in the figure and obtained by means of the usual algebraic transformations, given the fact that the folding of complex**numbers**you need in parts, and the square of the imaginary unit equal to negative one.5

Sometimes in missions you want to calculate modulus of complex

**number**. Make it easy. You need to take the square root of the sum of the real and imaginary part of a complex**number**. This will be the numerical value of the modulus of a complex**number**.Useful advice

In most cases, solve examples with complex numbers is possible without special knowledge of the formulas. It is sufficient to use the definition of complex numbers and the algebraic transformations.