In Mathematics, we have learned a variety of numbers such as counting numbers, even and odd numbers, integers, natural and whole numbers, etc. These numbers form the base of Maths. Each type of number has its own properties and importance.
Counting numbers are the most basic types of numbers that are used to count people or objects. It starts with 1,2,3,4,5, and so on. Even numbers are divisible by 2 but odd numbers are not.
Even: 2,4,6,8,10,..
Odd: 1,3,5,7,9,…
Integers are the numbers that are not fractions. They can be negative, positive, or zero. The only difference between natural numbers and whole numbers is that the whole numbers include zero.
Here, we are going to discuss real numbers and complex numbers along with examples.
What are Real Numbers?
In our real life, commonly we deal with real numbers. A real number can be any number that can be represented in a number line and can be extended indefinitely on both sides. These real numbers will include integers, natural numbers, whole numbers, rational numbers, irrational numbers. Let us understand them one by one.
Integers: As we discussed in the introduction, the integers are all the positive and negative natural numbers along with zero and it does not include fractions. The examples of integers are -2, -3, 0, 1, 4, etc.
Natural numbers: These are the positive integers that start from 1 and end at infinity. (Examples: 1,2,3,4,5,6,7,8,9,10,……)
Whole numbers: The combination of zero and natural numbers is the whole number. It starts with 0 and ends at infinity. (Examples: 0,1,2,3,4,5,6,…….).
Rational numbers: The numbers that can be expressed in the form of ratios such as P/Q, where P and Q are both integers and Q is not equal to 0. They are finite numbers and are repeating decimals. (Examples: ½, ¾, ⅚, 9/8, etc.)
Irrational numbers: The numbers that are not rational are called irrational numbers. These numbers are non-repeating decimals with no termination. (Examples: √2, √3, 0.212112111…, π, etc.)
All the types explained above are basically the subsets of real numbers. The numbers are real because we can easily perform mathematical operations on them, such as addition, subtraction, multiplication and division.
What are Complex Numbers?
Complex numbers are the ones that are not real. They are the combination of real numbers and imaginary numbers. These imaginary numbers cannot be simplified. Therefore, such numbers that include imaginary parts are called complex numbers.
A complex number is usually represented as “A+iB”. Here,
- Part 1: “A” is the real part
- Part 2: “iB” is the imaginary part
The value of i is equal to the square root of -1.
I.e. i = √-1 or i2 = -1
Since we cannot conclude the square root of a negative number, therefore, i is an imaginary number.
Examples of complex numbers:
- 2 + 3i
- -3 + 4i
√2 – 6i
