Number System

TYPES OF NUMBER SYSTEM G S S SCHOOL KASSEL FROM. GURPREETKAUR MATH MISTRESS GUIDEDBY ARTI BIALA

INTRODUCTION Number (mathematics), word or symbol used to designate quantities or entities that behave like quantities.

TYPES OF NUMBERS 1. RATIONAL NUMBERS 2. IRRATIONAL NUMBERS 3. COMPLEX NUMBERS .

RATIONAL NUMBER The simplest numbers are the natural numbers, 1, 2, 3, .... The natural numbers are also called the whole numbers, positive integers, or positive rational integers. The natural numbers are closed with respect to addition and multiplication—that is, the sum and product of two natural numbers are always natural numbers. Because the quotient (the result of dividing) of two natural numbers, however, is not always a natural number, it is convenient to introduce the positive fractions to represent the quotient of any two natural numbers.

IRRATIONAL NUMBER 

The development of geometry indicated the need for more numbers; the length of the diagonal of a square with sides one unit long cannot be expressed as a rational number. Similarly, the ratio of the circumference to the diameter of a circle is not a rational number. These and other needs led to the introduction of the irrational numbers. A decimal expansion that is neither of the two types described above represents an irrational number.

COMPLEX NUMBER 

The product of a real number multiplied by itself is 0 or positive, so the equation x2 = -1 has no solutions in the real number system. If such a solution is desired, new numbers must be invented. Let i = Á be a new number representing a solution of the preceding equation. All numbers of the form a + bi, in which a and b are real numbers, belong to the complex number system.

DIGRAM OF COMPLEX NUMBER 

THANKS