Extracurricular lesson - number module. The absolute value of a number

a is the number itself. Number in module:

|a| = a

Modulus of a complex number.

Suppose there is complex number, which is written in algebraic form z=x+i·y, Where x And y- real numbers, which represent the real and imaginary parts of a complex number z, a is the imaginary unit.

Modulus of a complex number z=x+i·y is the arithmetic square root of the sum of the squares of the real and imaginary parts of a complex number.

The modulus of a complex number z is denoted as follows, which means that the definition of the modulus of a complex number can be written as follows: .

Properties of the module of complex numbers.

• Domain of definition: the entire complex plane.
• Range of values: }