Complex Numbers

Imaginary roots 

x^2 + 4 = 0

--> x ^ 2 = - 4 

--> x = √- 4

--> x = √4 * √- 1 

--> x = + 2 i or - 2 i where i = √ - 1 is called imaginary number which gave rise to an important branch of mathematics called Complex Numbers.....

Palindrome:-Example-7-10-2017

Please observe tomorrow's date 7-10-2017, as a  7102017,which is a "Palindrome".

It is an interesting sequence in Mathematics,which reads same forward as backward.

Cake made by me for my students who worked hard for Maths Competition on the occasion of Pi Approximation Day.

Pi -An irrational Number

Hey....You remember school mathematics???

Area of Circle = p r²    where  p =22/7 .
 Is it the true value of p ?
Actually it is the fraction whose value is very close to p which is equal to 3.14159.......................................
Now where does this end?Don't know. p is a very special number. Its decimal expansion has neither repeating pattern nor terminating decimal representation.
Thus, p is an irrational number and very special. So far scientists have discovered 10,000 digits after the decimal point for which a special computer is required to store such big number.
There are many applications of this special number p.
It is used in the construction of Pyramids.I have read somewhere that there is a shloka in Bhagvadgita, which on decoding gives the value of p upto 32 decimal places. This tells us how ancient is p andit was used in India long ago.
p has always fascinated me !!!
I hope you are also little bit motivated to discover more about p......

Factorization

     X³  -27=  (X-3) (X²+3X+9)

Two sets are called disjoint if they have no elements in common.

e. g. The set of even integers and the set of odd integers are disjoint sets as every integer is either odd or even but not both.  

Numbers

Square root of a number . . . 

Consider the equation 

x^2 -25=0, the solutions are 5&-5. Now consider ,  the equation x^2 +25=0. The solutions of this equation are square root of -25 which are not real numbers. As square root of a negative number is not real.  It is called as imaginary number. Square root of -1 is imaginary and is denoted by i .  The set of complex numbers is denoted by C and is of great importance in mathematics. 

Set of Natural Numbers :-

N = {1,2,3........}