Properties of Irrational Numbers

Previously we have discussed about factoring perfect square trinomials worksheet and In today's session we are going to discuss about Rational and irrational numbers which comes under board of andhra pradesh intermediate, They are the different type of number representation in the number system of mathematics. These are the number representations which help in solving the problem related to math. If we define the rational numbers then we can say that rational numbers are those numbers which represent the integer value in the form of numerator and denominator. For example, x / y, here x is numerator and y indicates the denominator which should be greater then 0.

In the same sense we can say that irrational numbers are those numbers which can’t be represented in the form of numerator and denominator format. In the general sense irrational numbers in the number system can be considered as real numbers but they can’t be shown in fractional format. The fundamental properties of irrational number is that they can’t be represented in ratio form.Through this topic we are going to discuss about the Properties of Irrational Numbers. Let's explain the concept to you with the help of some examples.

The famous example of irrational numbers is ∏. Generally this symbol is known as ‘ pi ‘. In the mathematics pi value is approximated as 22 / 7. It means ∏ = 3.141592653589 and so on. In the value of pi , we can see that the value is not accurate or they can’t be represented in standard fractional format. Thus, one of the Properties of Irrational Numbers is that the cannot be represented in fractional form. (Know more about  Irrational Numbers in broad manner, here,)

Another famous example of irrational numbers are √2. In the √2 there actual value is 1.41421356 and so on. As like the another fractional number √2 can’t be represented using ratio property of two numbers and they can’t be represented in any simple faction. That’s why this is irrational number.

Even the number e (symbol of Euler number ) can’t be represented in the ratio form and in simpler fraction from.

In the next session we are going to discuss subtracting integers worksheet 
and Read more maths topics of different grades such as Perfect Square Trinomials in the upcoming sessions here and You can visit our website for getting information about Rate of Change Formula.

 

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Properties of Complex Numbers

Previously we have discussed about system of equations worksheet and Today we are going to discuss about the Complex numbers and their properties which comes under andhra pradesh education board. First of all we should know about the complex numbers. A complex number is a number which has a form of x + iy, here x and y are the real numbers and i is known as the imaginary part or unit of the complex number. The value of i is root of -1 or i>2= -1. In the form of the complex number the term x is the real part and iy is the imaginary part of the number. The complex number is known as purely imaginary number if its real part or x is equals to 0.(Know more about Complex Numbers in broad manner, here,)
Now here I will tell you about some of the Properties of Complex Numbers:
1.    Powers of   i = root of -1, i>2 = -1, i>3 = -1, i>4 = 1
2.     Equality of two complex numbers: Two complex numbers are said to be equal if their real and imaginary parts are equal say two complex numbers are

 x + iy = a + ib if x = a and y = b.

3.    Addition property: When we add two complex numbers then we have to add the real parts to one another and imaginary parts to one another of the numbers. Like if we have two complex numbers say a + ib and x + iy then their addition will be (a + x) + (b + y)i.
The subtraction is just opposite of the addition property of the complex numbers.
4.    Multiplication: To multiply two complex numbers simply use the FOIL method.

(a + bi)*(x + yi)= (ax - by) + (ay + bx)i.

5.     Complex Conjugation: The complex number x + yi can be conjugate and it will give value x –yi. One thing is to remember is that the product of a complex number and its conjugate is always a real value. That is (x + iy) (x - iy)= x2+ y2.
So these are the Complex Number Properties. In the next topic we are going to discuss Properties of Numbers and if anyone want to know about Solving Binomial Expansion then they can refer to Internet and text books for understanding it more precisely and if you need help with math you can visit our website.